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+%%% amshelp.tex
+%%% This is an AMS-LaTeX file
+
+%%% Copyright (c) 2000 Philip S. Hirschhorn
+%
+% This document may be distributed and/or modified under the
+% conditions of the LaTeX Project Public License, either version 1.2
+% of this license or (at your option) any later version.
+% The latest version of this license is in
+%   http://www.latex-project.org/lppl.txt
+% and version 1.2 or later is part of all distributions of LaTeX 
+% version 1999/12/01 or later.
+%
+
+
+%%% Philip Hirschhorn
+%%% Department of Mathematics
+%%% Wellesley College
+%%% Wellesley, MA 02481
+%%% psh@poincare.wellesley.edu
+%%% psh@math.mit.edu
+
+
+%%% This is an attempt to explain how to get up and running with
+%%% AmS-LaTeX, if you've already got some familiarity with either 
+%%% TeX or AMS-TeX or LaTeX.
+
+
+
+
+\newcommand{\filedate}{August 10, 2000}
+\newcommand{\fileversion}{Version 2.0}
+
+%---------------------------------------------------------------------
+\documentclass[12pt]{amsart}
+%\documentclass{amsart}
+\usepackage{amscd}
+
+
+\newcommand{\tensor}{\otimes}
+\newcommand{\homotopic}{\simeq}
+\newcommand{\homeq}{\cong}
+\newcommand{\iso}{\approx}
+\newcommand{\ho}{\operatorname{Ho}}
+
+
+
+
+\newcommand{\C}{{\cal C}}
+\newcommand{\M}{{\cal M}}
+\newcommand{\W}{{\cal W}}
+
+
+\newenvironment{technical}{\begingroup \small}{\endgroup}
+
+
+
+%---------------------------------------------------------------------
+%---------------------------------------------------------------------
+
+\numberwithin{equation}{section}
+
+
+%       Theorem environments
+
+\theoremstyle{plain} %% This is the default, anyway
+\newtheorem{thm}[equation]{Theorem}
+\newtheorem{cor}[equation]{Corollary}
+\newtheorem{lem}[equation]{Lemma}
+\newtheorem{prop}[equation]{Proposition}
+
+
+\theoremstyle{definition}
+\newtheorem{defn}[equation]{Definition}
+
+\theoremstyle{remark}
+\newtheorem{rem}[equation]{Remark}
+\newtheorem{ex}[equation]{Example}
+\newtheorem{notation}[equation]{Notation}
+\newtheorem{terminology}[equation]{Terminology}
+
+
+
+
+%---------------------------------------------------------------------
+%---------------------------------------------------------------------
+%---------------------------------------------------------------------
+%---------------------------------------------------------------------
+
+\begin{document}
+
+
+\title[Running \AmS-\LaTeX]
+{Getting up and running\\
+with \AmS-\LaTeX}
+
+\author{Philip S. Hirschhorn}
+
+\address{Department of Mathematics\\
+         Wellesley College\\
+         Wellesley, Massachusetts 02481}
+
+\email{psh@math.mit.edu}
+
+
+\date{\filedate, \fileversion}
+
+
+\begin{abstract}
+  This is an attempt to tell you enough about \LaTeX{} and
+  \AmS-\LaTeX{} so that you can get started with it \emph{without}
+  having to read the book.
+\end{abstract}
+
+\maketitle
+
+
+
+
+\tableofcontents
+%---------------------------------------------------------------------
+%---------------------------------------------------------------------
+\section{Introduction}
+
+This is an attempt to get you up and running with \AmS-\LaTeX{} with
+the least possible pain.  These instructions won't be a substitute for
+the User's Guide, but they may get you started quickly enough so that
+you'll only need to refer to the guide occasionally, which should
+eliminate most of the pain.
+
+The current version of \AmS-\LaTeX{} (version 1.2) is really just an
+optional package for the new standard \LaTeX.  \AmS-\LaTeX{} provides
+the document classes \verb"amsart" and \verb"amsbook" (see
+Section~\ref{sec:DocClsCom}) to replace the standard document classes
+\verb"article" and \verb"book", and an optional package \verb"amsmath"
+that can be used with the standard \LaTeX{} document classes.  Thus,
+using \AmS-\LaTeX{} is really using a variety of \LaTeX.  If you're
+new to \LaTeX{}, and these last few sentences made no sense to you at
+all, don't worry about it.  You don't have to know what the standard
+\LaTeX{} document classes are in order to use the \AmS-\LaTeX{}
+replacements for them.
+
+
+I'll be assuming that you have at least some experience with either
+plain \TeX, \AmS-\TeX{} or \LaTeX, and I'll try to tell you what you
+need to know so that you can get started with \AmS-\LaTeX{}
+\emph{without} actually reading the \LaTeX{} User's
+Guide~\cite{latex}, or even taking much of a look at the \AmS-\LaTeX{}
+User's Guide~\cite{amslatexusersguide}.
+
+
+If you've never used \emph{any} version of \TeX, then I recommend
+``The not so short introduction to \LaTeXe{}'', by Tobias Oetiker,
+Hubert Partl, Irene Hyna, and Elisabeth Schlegl \cite{NotShort}.  This
+is intended for those with no knowledge of \TeX{} or \LaTeX, and
+concisely gives a description of what a \LaTeX{} document looks like
+and how you type text and simple mathematics in a \LaTeX{} document.
+
+I've also given you a template file \verb"template.tex", which is an
+attempt to give you enough to mostly fake your way through an
+\AmS-\LaTeX{} file, \emph{almost} without even reading these
+instructions.  I've included the text of that file in these
+instructions as Section~\ref{sec:template}, so you might want to take a
+look at that now, and then just use the table of contents of these
+instructions to get more information on whatever in that file
+confuses you.
+
+In case you haven't guessed, these instructions were printed using
+\AmS-\LaTeX, so you can get some idea what it all looks like.
+
+
+
+%---------------------------------------------------------------------
+%---------------------------------------------------------------------
+\section{Basic \LaTeX{} stuff}
+\label{sec:basicstuff}
+
+In this section, we'll describe the three commands that have to be
+part of any \LaTeX{} document: \verb"\documentclass",
+\verb"\begin{document}", and \verb"\end{document}".  The complete
+explanation of these can be found in the \LaTeX{} User's
+Guide~\cite{latex} or in \emph{The not so short introduction to
+  \LaTeXe}~\cite{NotShort}.  We'll also explain how to begin a new
+section or subsection of the paper, and how \LaTeX{} manages to get
+the cross-references right (which is also the explanation of why you
+need to run a file through \LaTeX{} \emph{twice} to be sure that all
+the cross-references are correct).
+
+
+\subsection{The  \texttt{documentclass} command}
+\label{sec:DocClsCom}
+
+Before you type anything that actually appears in the paper, you must
+include a \verb"\documentclass" command.  It's easiest to just put the
+\verb"\documentclass" command at the very beginning of the file,
+possibly with a few lines of comments before it.
+
+It's actually the choice of document class that determines whether
+you're using \AmS-\LaTeX{} or just plain old \LaTeX.  There are two
+document classes that are a part of \AmS-\LaTeX: \verb"amsart" and
+\verb"amsbook".  There is also the \verb"amsmath" package that can be
+used with the standard \LaTeX{} \verb"article" document class.  I'll
+only be discussing the \verb"amsart" document class here.  For the
+others, see the \AmS-\LaTeX{} User's Guide~\cite{amslatexusersguide}.
+
+
+The simplest version of the \verb"documentclass" command is
+\begin{center}
+\verb"\documentclass{amsart}"
+\end{center}
+This will give you the default type size, which is 10~point type.  If
+you'd like to use 12~point type, then you should include the optional
+argument \verb"[12pt]"; this makes the command
+\begin{center}
+\verb"\documentclass[12pt]{amsart}"
+\end{center}
+
+
+There are at least two optional packages that might be of interest.
+The first is for when you want to include the macros that make it
+easier to draw commutative diagrams.  (These aren't included
+automatically, since they take up a lot of memory, and not everyone
+wants to use them.)  If you want 10~point type and you want to use the
+commutative diagram macros, then the commands to use are
+\begin{center}
+  \begin{tabular}{l}
+    \verb"\documentclass{amsart}"\\
+    \verb"\usepackage{amscd}"
+  \end{tabular}
+\end{center}
+If you want 12~point type and you want to use the commutative
+diagram macros, then the commands are
+\begin{center}
+  \begin{tabular}{l}
+    \verb"\documentclass[12pt]{amsart}"\\
+    \verb"\usepackage{amscd}"
+  \end{tabular}
+\end{center}
+
+
+The other optional package is for use when you want to use some of the
+special symbols contained in the \AmS-Fonts package.  (These are the
+fonts \verb"msam" and \verb"msbm".)  If you want the standard names
+for these symbols to be defined for your use, then you need to use the
+optional package \verb"amssymb".  Thus, to use the default 10~point
+type and have the special symbols defined, use the commands
+\begin{center}
+  \begin{tabular}{l}
+    \verb"\documentclass{amsart}"\\
+    \verb"\usepackage{amssymb}"
+  \end{tabular}
+\end{center}
+If you want to use 12~point type, the commutative diagram macros, and
+special symbols from the \AmS-Fonts collection, then use the commands
+\begin{center}
+  \begin{tabular}{l}
+    \verb"\documentclass[12pt]{amsart}"\\
+    \verb"\usepackage{amssymb}"
+  \end{tabular}
+\end{center}
+This document uses both of these packages, and so we used the commands
+\begin{center}
+  \begin{tabular}{l}
+    \verb"\documentclass[12pt]{amsart}"\\
+    \verb"\usepackage{amscd}"\\
+    \verb"\usepackage{amssymb}"
+  \end{tabular}
+\end{center}
+
+%---------------------------------------------------------------------
+
+\subsection{\texttt{begin\{document\}} and \texttt{end\{document\}}}
+
+Everything that is to appear in the document must appear in between
+the \verb"\begin{document}" and \verb"\end{document}" commands. There
+are no optional arguments for these commands, so they always look the
+same.  Anything following the \verb"\end{document}" command is
+ignored.  You \emph{are} allowed to have macro definitions (i.e.,
+newcommands; see Section~\ref{sec:definitions}) before the
+\verb"\begin{document}", and that's actually a good place for them,
+  but that's about all.
+
+%---------------------------------------------------------------------
+\subsection{Sections and subsections}
+\label{sec:sections}
+
+To begin a new section, you give the command
+\begin{center}
+\verb"\section{Section name}"
+\end{center}
+To begin the present section, I gave the command
+\begin{center}
+\verb"\section{Basic \LaTeX{} stuff}"
+\end{center}
+A section number is supplied automatically.  If you want to be able to
+make reference to that section, then you need to \emph{label} it.
+Since I wanted to be able to demonstrate the cross-reference commands,
+I actually began this section with the lines
+\begin{center}
+  \begin{tabular}{l}
+    \verb"\section{Basic \LaTeX{} stuff}"\\
+    \verb"\label{sec:basicstuff}"
+  \end{tabular}
+\end{center}
+This allows me to say ``\verb"Section~\ref{sec:basicstuff}"'' and have
+it printed as Section~\ref{sec:basicstuff}.
+
+To begin a new subsection, you give the command
+\begin{center}
+\verb"\subsection{Subsection name}"
+\end{center}
+To begin the present subsection, I gave the command
+\begin{center}
+\verb"\subsection{Sections and subsections}"
+\end{center}
+A subsection number is supplied automatically.  If you want to be able
+to make reference to that subsection, then you need to \emph{label}
+it.  This subsection was begun with the lines
+\begin{center}
+  \begin{tabular}{l}
+    \verb"\subsection{Sections and subsections}"\\
+    \verb"\label{sec:sections}"
+  \end{tabular}
+\end{center}
+so if we say ``\verb"Section~\ref{sec:sections}",'' it is printed as
+Section~\ref{sec:sections}.
+
+Labels always take the number of the smallest enclosing structure.
+Thus, a \verb"\label" command that's inside a section but \emph{not}
+inside a subsection or Theorem or anything else will take the value of
+the section counter, while a \verb"\label" command that's inside the
+statement of a Theorem will take the value of that Theorem number.
+For more information on this, see Section~\ref{sec:xreferences}.
+
+%--------------------------------------------------------------------
+\subsubsection{Yes, there are subsubsections too}
+
+I began this subsubsection with the command
+\begin{center}
+\verb"\subsubsection{Yes, there are subsubsections too}"
+\end{center}
+I refuse to even experiment to see if there are subsubsubsections.
+
+
+
+%--------------------------------------------------------------------
+\subsubsection*{Sections without numbers}
+
+I began this subsubsection with the command
+\begin{center}
+\verb"\subsubsection*{Sections without numbers}"
+\end{center}
+and got a subsubsection that wasn't numbered.  If you give the command
+\begin{center}
+\verb"\section*{A Section Title}"
+\end{center}
+then you'll begin a new section that will not have a number.
+
+
+
+%---------------------------------------------------------------------
+\subsection{Italics \emph{for emphasis}}
+
+If you want to use italics to emphasize a word or two, the \LaTeX{}
+convention is not to switch explicitly to italics, but rather to use
+the command \verb"\emph" (which means \emph{emphasize}).  This command
+works just like a font change command, except that it switches you
+\emph{into} italics if the current font is upright, and switches you
+\emph{out of} italics if the current font is italics.
+
+For example, if you type
+\begin{center}
+\verb"The whole is \emph{more} than the sum of its parts."
+\end{center}
+you'll get
+\begin{center}
+The whole is \emph{more} than the sum of its parts.
+\end{center}
+but if you type
+\begin{verbatim}
+\begin{thm}
+  The whole is \emph{more} than the sum of its parts.
+\end{thm}
+\end{verbatim}
+you'll get
+\begin{thm}
+  The whole is \emph{more} than the sum of its parts.
+\end{thm}
+
+
+\subsubsection*{Note}
+
+The \verb"\emph" command is a recent addition to \LaTeX, and it has
+the feature that it automatically inserts an italic correction where
+needed.  If you don't know what an italic correction is, you can
+safely ignore this paragraph (but I will at least mention that all
+those ``\verb"\/"'' commands frequently seen in \TeX{} (and older
+\LaTeX) documents are all inserting italic corrections; the point of
+this paragraph is that, with the current version of \LaTeX, you don't
+have to do that anymore).
+
+
+
+%---------------------------------------------------------------------
+\subsection{Once is never enough}
+
+This is an explanation of how \LaTeX{} manages to fill in
+cross-references to parts of the file it hasn't processed yet, and
+what those \verb".aux" and \verb".toc" files are.
+
+
+\subsubsection*{Cross-References}
+
+Every time \LaTeX{} processes your file, it writes an \emph{auxiliary}
+file.  Since the file containing these instructions is called
+\verb"amshelp.tex", the auxiliary file is called \verb"amshelp.aux".
+The auxiliary file contains the definitions of all the keys used for
+cross-references.  When \LaTeX{} begins to process your file, it first
+looks for an \verb".aux" file, and reads it in if it exists.  Of
+course, this is the \verb".aux" file that was produced the \emph{last}
+time that your file was processed, so the Theorem numbers, Section
+numbers, etc., are all the ones from the last time the file was
+processed.
+
+The very first time that \LaTeX{} processes your file, there is no
+\verb".aux" file, and so \LaTeX{} gives \emph{lots} of warning
+messages about undefined labels, or whatever.  Ignore all of this.
+The \emph{next} time that you run \LaTeX, there \emph{will} be an
+\verb".aux" file, and all the references will be filled in.  (Yes, it
+is possible, at least in theory, for some page number to change every
+time you run \LaTeX{} on your file, even without any changes in the
+source file, but this isn't very likely.)
+
+\subsubsection*{The Table of Contents}
+
+If you give the command \verb"\tableofcontents", then \LaTeX{} will
+try to write a table of contents, including the page numbers of the
+sections.  Obviously, \LaTeX{} can't know those page numbers or
+section titles yet, so as \LaTeX{} processes your file, it writes a
+\verb".toc" file containing the information it needs.  (The
+\verb".toc" file for these instructions is \verb"amshelp.toc".)  Once
+again, \LaTeX{} is always using the information from the \emph{last}
+time that it processed your file.
+
+If you \emph{do} include a table of contents in your document, and if
+the table of contents takes up at least a page or so of space, then
+you might have to run \LaTeX{} \emph{three} times in order to get all
+of the cross-references right.  The reason for this is that the first
+time you run \LaTeX{} there isn't any \verb".toc" file listing the
+section titles, and so the table of contents has nothing in it.  The
+second time you run \LaTeX{} you'll get a table of contents that lists
+the page numbers for the sections from the last time you ran \LaTeX,
+when the table of contents took up no space at all.  Unfortunately,
+during this second run, the table of contents will be created, and
+will take up enough space to change the page numbers of the sections
+from what they were during the first run.  Only during the
+\emph{third} run will the correct page numbers be written into the
+table of contents.  Since this doesn't change the amount of space that
+the table of contents occupies, this version will be correct.
+
+\subsubsection*{How do I know when everything is correct?}
+
+After processing your file, \LaTeX{} checks whether all the
+cross-reference numbers that it read from the \verb".aux" file are
+correct.  If any of them are incorrect, it prints a warning on the
+screen at the very end of the run advising you that labels may have
+changed, and that you should run \LaTeX{} again to get the
+cross-references right.  Unfortunately, \LaTeX{} doesn't seem to check
+that the table of contents entries are correct, so if you change the
+name of a section in a way that doesn't make any page references
+incorrect, you won't be warned to run \LaTeX{} again.
+
+
+
+
+
+%---------------------------------------------------------------------
+%---------------------------------------------------------------------
+\section{Title, Author,  and the \texttt{maketitle} command}
+
+This stuff should go right after the \verb"\begin{document}" command.
+  I'll give a quick sketch here, which is probably all you'll ever
+  need, but the full explanation is given in \emph{Instructions for
+    preparation of papers and monographs: \AmS-\LaTeX} \cite{instr-l}.
+  If you are already familiar with \LaTeX, then you should be warned
+  that this part is slightly different from what you do when using the
+  standard \LaTeX{} \verb"article" documentclass.
+
+%---------------------------------------------------------------------
+
+\subsection{The title}
+You announce the title with the
+command
+\begin{center}
+\verb"\title[Optional running title]{Actual title}"
+\end{center}
+These instructions used the title command
+\begin{center}
+  \begin{tabular}{l}
+    \verb"\title[Running \AmS-\LaTeX]"\\
+    \verb"{Getting up and running\\"\\
+    \verb"with \AmS-\LaTeX}"
+  \end{tabular}
+\end{center}
+Notice that you indicate line breaks in the title with a double
+backslash.  If I had decided to let the \emph{full} title be printed
+in the head of the odd numbered pages, I would have used the command
+\begin{center}
+  \begin{tabular}{l}
+    \verb"\title{Getting up and running\\"\\
+    \verb"with \AmS-\LaTeX}"
+  \end{tabular}
+\end{center}
+
+
+
+%---------------------------------------------------------------------
+\subsection{The author, and the author's address}
+
+
+The author is specified with an \verb"author" command:
+\begin{center}
+\verb"\author{Author's name}"
+\end{center}
+These directions used the command
+\verb"\author{Philip S. Hirschhorn}".
+The author's address is given in an address command, with double
+backslashes to indicate line breaks.  These instructions used the
+command
+\begin{center}
+  \begin{tabular}{l}
+    \verb"\address{Department of Mathematics\\"\\
+    \verb"Wellesley College\\"\\
+    \verb"Wellesley, Massachusetts 02481}"
+  \end{tabular}
+\end{center}
+If the author's current address is different from the address at which
+the research was carried out, then you can specify the current address
+with the command \verb"\curraddr".  For example, you might say
+\begin{center}
+  \begin{tabular}{l}
+    \verb"\curraddr{Department of Mechanics\\"\\
+    \verb"Brake and Wheel Bearing Division\\"\\
+    \verb"Serene Service Center\\"\\
+    \verb"Salem, Massachusetts 02139}"
+  \end{tabular}
+\end{center}
+You can also include an email address, with the \verb"\email"
+command.  These instructions used the command
+\begin{center}
+  \verb"\email{psh@math.mit.edu}"
+\end{center}
+To acknowledge support, use the command \verb"\thanks", e.g.,
+\begin{center}
+  \verb"\thanks{Supported in part by NSF grant 3.14159}"
+\end{center}
+This will be printed as a footnote on the first page.
+
+
+
+
+
+\subsubsection*{Multiple authors}
+
+If there are several authors, then each one should have a separate
+\verb"\author" command, with each individual's address (and current
+address, and email address) following that individual's \verb"\author"
+command, in its own \verb"\address" command (and \verb"\curraddr"
+command, and \verb"\email" command).  If there \emph{are} several
+authors, and their combined names are too long for the running head on
+the even numbered pages, you can give an optional argument to each
+\verb"\author" command to supply a shortened form to use in the
+running head.  (It's apparently a convention that the running head in
+a multiple author paper should have only initials for the first and
+middle names, but I don't think that I was invited to that
+convention.)
+
+
+%---------------------------------------------------------------------
+
+\subsection{The date}
+
+This is pretty straightforward:
+\begin{center}
+\verb"\date{Whatever date you please}"
+\end{center}
+To have the date of processing used, use the command
+\verb"\date{\today}".
+
+%---------------------------------------------------------------------
+\subsection{\texttt{maketitle}}
+
+
+After you've given all of the commands mentioned in this section, you
+can give the command \verb"\maketitle".  The exact arrangement is
+determined by the document class.  In particular, the \verb"amsart"
+document class puts the author's address at the \emph{end} of the
+paper.  If you \emph{don't} give the command \verb"\maketitle", a
+title won't be made.
+
+
+
+%---------------------------------------------------------------------
+%---------------------------------------------------------------------
+\section{Theorems, Propositions, Lemmas, etc.}
+
+The instructions in this section assume that you're using the
+\verb"newtheorem" commands that I put in the file
+\verb"template.tex".
+
+\subsection{Stating theorems, propositions, etc.}
+
+To state a theorem, you do the following:
+\begin{verbatim}
+\begin{thm}
+The square of the hypotenuse of a right triangle
+is equal to the sum of the squares of the two
+adjacent sides.
+\end{thm}
+\end{verbatim}
+If you do that, you'll get the following:
+\begin{thm}
+\label{pythagthm}
+The square of the hypotenuse of a right triangle
+is equal to the sum of the squares of the two
+adjacent sides.
+\end{thm}
+If you thought that it was only a proposition, you'd use
+\begin{verbatim}
+\begin{prop}
+The square of the hypotenuse of a right triangle
+is equal to the sum of the squares of the two
+adjacent sides.
+\end{prop}
+\end{verbatim}
+and you'd get
+\begin{prop}
+The square of the hypotenuse of a right triangle
+is equal to the sum of the squares of the two
+adjacent sides.
+\end{prop}
+
+If you think it's a theorem again, but you'd like to make reference to
+it in some other part of the paper, you have to choose a \emph{key}
+with which you'll refer to it, and then \emph{label} the theorem.  If
+you want to use the key \emph{pythagthm}, then it would look like the
+following:
+\begin{verbatim}
+\begin{thm}
+\label{pythagthm}
+The square of the hypotenuse of a right triangle
+is equal to the sum of the squares of the two
+adjacent sides.
+\end{thm}
+\end{verbatim}
+If you later give the command \verb"\ref{pythagthm}", then that
+command will expand to the \emph{number} that was assigned to that
+theorem (in this case, \ref{pythagthm}).  For more explanation of
+cross-references, see Section~\ref{sec:xreferences}.
+
+If you'd like to state a theorem and give a \emph{name} to it, then
+you can add an optional argument to the \verb"\begin{thm}" command. 
+If you type
+\begin{verbatim}
+\begin{thm}[Pythagorus]
+The square of the hypotenuse of a right triangle
+is equal to the sum of the squares of the two
+adjacent sides.
+\end{thm}
+\end{verbatim}
+you'll get
+\begin{thm}[Pythagorus]
+The square of the hypotenuse of a right triangle
+is equal to the sum of the squares of the two
+adjacent sides.
+\end{thm}
+
+
+\subsubsection*{Summary of environments provided in the template}
+
+All of the following structures are numbered in the same sequence,
+in the form SectionNumber.Number.  Equations (i.e., displayed
+formulas, whether they are equations or not) will be numbered in the
+same sequence.
+
+$$
+\begin{tabular}{c@{\hspace{4em}}l@{\hspace{4em}}c}
+
+\multicolumn{3}{c}{Theorem Environments}\\*[8pt]
+
+\hspace{1em}Name&  Printed Form& Body font\\*[6pt]
+
+\texttt{thm}&           \textbf{Theorem}&      Italic\\
+\texttt{cor}&           \textbf{Corollary}&    Italic\\
+\texttt{lem}&           \textbf{Lemma}&        Italic\\
+\texttt{prop}&          \textbf{Proposition}&  Italic\\
+\texttt{defn}&          \textbf{Definition}&   Normal\\
+\texttt{rem}&           \textit{Remark}&       Normal\\
+\texttt{ex}&            \textit{Example}&      Normal\\
+\texttt{notation}&      \textit{Notation}&     Normal\\
+\texttt{terminology}&   \textit{Terminology}&  Normal\\*[3pt]
+\end{tabular}
+$$
+
+For full details, see the beginning of the template file (reproduced
+here in Section~\ref{sec:template}), after the comment ``The Theorem
+Environments.''
+
+
+
+%---------------------------------------------------------------------
+\subsection{Proofs}
+
+To give a proof, you do the following:
+\begin{verbatim}
+\begin{proof}
+As any fool can plainly see, it's true!
+\end{proof}
+\end{verbatim}
+and you'll get the following:
+\begin{proof}
+As any fool can plainly see, it's true!
+\end{proof}
+If the theorem said that a condition was both necessary and sufficient
+for something, and you want to prove each part separately,
+you can do the following:
+\begin{verbatim}
+\begin{proof}[Proof (sufficiency)]
+Well, it's \emph{obviously} sufficient!
+\end{proof}
+\end{verbatim}
+and you'll get
+\begin{proof}[Proof (sufficiency)]
+Well, it's \emph{obviously} sufficient!
+\end{proof}
+that is, the \verb"proof" environment allows you to use an optional
+second argument that will appear in place of the word \verb"Proof".
+
+If the proof of Theorem~\ref{pythagthm} does not appear immediately
+after its statement, you might use the following:
+\begin{verbatim}
+\begin{proof}[Proof of Theorem~\ref{pythagthm}]
+As any fool can plainly see, it's true!
+\end{proof}
+\end{verbatim}
+and you'd get
+\begin{proof}[Proof of Theorem~\ref{pythagthm}]
+As any fool can plainly see, it's true!
+\end{proof}
+
+
+
+%---------------------------------------------------------------------
+%---------------------------------------------------------------------
+\section{Cross-References}
+\label{sec:xreferences}
+
+This section explains how to make reference to numbered sections,
+theorems, equations, and bibliography items, with the correct
+reference numbers filled in automatically by \LaTeX.
+
+%---------------------------------------------------------------------
+\subsection{References to sections, theorems and equations}
+\label{sec:thmrefs}
+
+For each structure in the manuscript to which you'll be making
+reference, you must assign a \emph{key} that you'll use to refer to
+that structure.  For sections, theorems and numbered equations, you
+assign the key using the \verb"\label" command.  This command takes
+one argument, which is the \emph{key} you're assigning to the object.
+The command \verb"\ref{key}" then produces the number that was
+assigned to that structure.  If the structure is an equation, then the
+command \verb"\eqref{key}" should be used instead of the command
+\verb"\ref{key}".
+
+
+Consider the following example.
+\begin{thm}
+\label{homotopy}
+If the maps $f\colon X \to Y$ and $g\colon X \to Y$ are homotopic,
+then $f_* = g_* \colon \mathrm{H}_*X \to \mathrm{H}_*Y$.
+\end{thm}
+
+We typed this theorem as follows.
+\begin{verbatim}
+\begin{thm}
+\label{homotopy}
+If the maps $f\colon X \to Y$ and $g\colon X \to Y$ are
+homotopic, then 
+$f_* = g_* \colon \mathrm{H}_*X \to \mathrm{H}_*Y$.
+\end{thm}
+\end{verbatim}
+If we now type ``\verb"see Theorem~\ref{homotopy}",'' then it will be
+printed as ``see Theorem~\ref{homotopy}.''
+
+
+
+
+
+\subsubsection*{So, what exactly is the label labeling?}
+
+We began this section by typing
+\begin{center}
+  \begin{tabular}{l}
+    \verb"\section{Cross-References}"\\
+    \verb"\label{sec:xreferences}"
+  \end{tabular}
+\end{center}
+and we began this subsection by typing
+\begin{center}
+  \begin{tabular}{l}
+    \verb"\subsection{References to sections, theorems and equations}"\\
+    \verb"\label{sec:thmrefs}"
+  \end{tabular}
+\end{center}
+The phrase ``\verb"See Section~\ref{sec:xreferences}"'' is printed as
+``See Section~\ref{sec:xreferences},'' while the phrase 
+``\verb"See Section~\ref{sec:thmrefs}"'' is printed as ``See
+Section~\ref{sec:thmrefs}.''
+
+
+The command \verb"\label{key}" assigns to \verb"key" the value of the
+\emph{smallest enclosing structure}.  That's why the command
+\verb"\ref{sec:xreferences}" is printed as~\ref{sec:xreferences},
+while \verb"\ref{sec:thmrefs}" is printed as~\ref{sec:thmrefs}: the
+key \verb"sec:xreferences" was defined inside of
+Section~\ref{sec:xreferences} but \emph{outside} of
+Section~\ref{sec:thmrefs}, while the key \verb"sec:thmrefs" was
+defined \emph{inside} of Section~\ref{sec:thmrefs}.
+
+
+\subsubsection*{References to equations}
+
+To make reference to a numbered equation, you assign the \emph{key}
+as before, but you replace \verb"\ref" with \verb"\eqref".  For
+example, if you type
+\begin{verbatim}
+\begin{equation}
+\label{additivity}
+\mathrm{H}_* \bigvee_{\alpha\in A} X_\alpha   \iso
+          \bigoplus_{\alpha\in A}\mathrm{H}_* X_\alpha
+\end{equation}
+\end{verbatim}
+then you'll get
+\begin{equation}
+\label{additivity}
+\mathrm{H}_* \bigvee_{\alpha\in A} X_\alpha   \iso
+          \bigoplus_{\alpha\in A}\mathrm{H}_* X_\alpha
+\end{equation}
+If we now say
+\begin{verbatim}
+\begin{thm}
+Equation~\eqref{additivity} is true for all sorts of
+functors $\mathrm{H}$.
+\end{thm}
+\end{verbatim}
+then we'll get
+\begin{thm}
+Equation~\eqref{additivity} is true for all sorts of
+functors $\mathrm{H}$.
+\end{thm}
+Notice the parentheses around the equation number, and the fact that
+even though the theorem is set in slanted type, the equation
+number is set in an upright font.  This is the advantage of using
+\verb"\eqref" instead of \verb"\ref"; the command \verb"\eqref"
+arranges it so that the number and surrounding parentheses are in an
+upright font no matter what the surrounding font, and supplies an
+italic correction if it's needed.
+
+
+%---------------------------------------------------------------------
+\subsection{References to page numbers}
+
+If you want to make reference to the \emph{page} that contains a
+label, rather than to the structure that is labeled, use the command
+\verb"\pageref{key}".  For example, if you type
+\begin{verbatim}
+Look at page~\pageref{homotopy} to find
+Theorem~\ref{homotopy}.
+\end{verbatim}
+you'll get ``Look at page~\pageref{homotopy} to find
+Theorem~\ref{homotopy}.''
+
+
+
+
+
+
+
+%---------------------------------------------------------------------
+\subsection{Bibliographic references}
+\label{sec:bibreferences}
+
+
+Bibliography entries receive a \emph{key} as part of their basic
+structure.  Each item in the bibliography is entered as
+\begin{verbatim}
+\bibitem{key} The actual bibliography item goes here.
+\end{verbatim}
+(For more detail on this, see Section~\ref{sec:bibliography}.)
+
+You refer to bibliography items using the \verb"\cite" command.  For
+example, the bibliography of these instructions contains the entry
+%
+\begin{verbatim}
+\bibitem{HA}
+D. G. Quillen, \emph{Homotopical Algebra,} Lecture Notes in
+Mathematics number 43, Springer-Verlag, Berlin, 1967.
+\end{verbatim}
+%
+If we say ``\verb"This is the work of Quillen~\cite{HA}",'' then it
+will be printed as ``This is the work of Quillen~\cite{HA}.''  Notice
+that square brackets have been inserted around the bibliography item
+number.
+
+The \verb"\cite" command takes an optional argument, which allows you
+to annotate the reference.  If we say
+``\verb"see~\cite[Chapter I]{HA}"'', then it will be printed as
+``see~\cite[Chapter I]{HA}''.
+
+
+
+
+
+%---------------------------------------------------------------------
+%---------------------------------------------------------------------
+\section{Mathematics}
+
+
+\subsection{Mathematics in running text}
+
+This is pretty much exactly as it is in plain \TeX, except that you
+have an extra option (which you can ignore).  The simplest thing is to
+just enclose between dollar signs (\verb"$") any material that should
+be in math mode.  Thus, if you type
+\begin{center}
+\verb"Let $f\colon X \to Y$ be a continuous function."
+\end{center}
+you'll get
+\begin{center}
+Let $f\colon X \to Y$ be a continuous function.
+\end{center}
+
+The only novelty that \LaTeX{} introduces is that, instead of using
+a dollar sign  to toggle math mode on and off, you can use
+`\verb"\("' to \emph{begin} math mode, and `\verb"\)"' to \emph{end}
+math mode.  Thus, the example above is equivalent to typing
+\begin{center}
+\verb"Let \(f\colon X \to Y\) be a continuous function."
+\end{center}
+This provides a tiny bit more error checking, but can
+otherwise be safely ignored.
+
+
+%---------------------------------------------------------------------
+\subsection{Displayed mathematics}
+
+For simple displayed mathematics without an equation number, this is
+very much like plain \TeX, again with extra choices that can be
+ignored.  If you enclose material between double dollar
+signs(\verb"$$"), it will be interpreted in math mode and displayed.
+Thus, if you've previously given the command
+\begin{center}
+  \verb"\newcommand{\iso}{\approx}"
+\end{center}
+(see Section~\ref{sec:definitions}), and you type
+\begin{verbatim}
+$$
+\pi_1(X \vee Y) \iso \pi_1X * \pi_1Y
+$$
+\end{verbatim}
+you'll get
+$$
+\pi_1(X \vee Y) \iso \pi_1X * \pi_1Y
+$$
+The new choices are that exactly the same thing will be obtained by
+either
+\begin{verbatim}
+\[
+\pi_1(X \vee Y) \iso \pi_1X * \pi_1Y
+\]
+\end{verbatim}
+or by
+\begin{verbatim}
+\begin{displaymath}
+\pi_1(X \vee Y) \iso \pi_1X * \pi_1Y
+\end{displaymath}
+\end{verbatim}
+or by
+\begin{verbatim}
+\begin{equation*}
+\pi_1(X \vee Y) \iso \pi_1X * \pi_1Y
+\end{equation*}
+\end{verbatim}
+
+
+If you'd like the displayed formula to be \emph{numbered}, then you
+should use the \verb"equation" environment.  (\LaTeX{} calls all
+formula numbers \emph{equation numbers}, whether or not the
+mathematics has anything to do with equations.)  If you type
+\begin{verbatim}
+\begin{equation}
+\pi_1(X \vee Y) \iso \pi_1X * \pi_1Y
+\end{equation}
+\end{verbatim}
+you'll get
+\begin{equation}
+\label{pi1eqn}
+\pi_1(X \vee Y) \iso \pi_1X * \pi_1Y
+\end{equation}
+(Notice that the \verb"equation" environment produces an equation
+number, while the \verb"equation*" environment doesn't.  This is a
+standard \LaTeX ism: Adding an asterisk to the name of a numbered 
+\LaTeX{} environment often gives the unnumbered equivalent.)
+
+
+If you'd like to be able to make reference to the equation number,
+you need to \emph{label} the equation, using a \emph{key} that you
+can use for referencing it:
+\begin{verbatim}
+\begin{equation}
+\label{pi1eqn}
+\pi_1(X \vee Y) \iso \pi_1X * \pi_1Y
+\end{equation}
+\end{verbatim}
+If you later type ``\verb"see formula~\eqref{pi1eqn}"'' you'll get 
+``see formula~\eqref{pi1eqn}.''  (For more on cross-references to
+formulas, see Section~\ref{sec:thmrefs}.)
+
+\AmS-\LaTeX{} has several environments that make it easier to typeset
+complicated multi-line displays.  These are explained in the
+\AmS-\LaTeX{} User's Guide~\cite{amslatexusersguide} and illustrated
+in \verb"testmath.tex"~\cite[pages 29--40]{testmath}.
+
+
+
+%---------------------------------------------------------------------
+\subsection{Commutative diagrams}
+
+\AmS-\LaTeX{} provides the \verb"CD" environment for drawing
+commutative diagrams.  These only allow for \emph{rectangular}
+diagrams, but they're very convenient to use.  If you need diagonal
+arrows, or curving arrows, or arrows that make a number of right angle
+turns, I recommend the XY-Pic package, which can do all of these
+things (and more).
+
+\textbf{Important}: To use the \verb"CD" environment, you need to load
+it with the command \verb"\usepackage{amscd}".  For example, the
+template file gives the commands
+\begin{center}
+  \begin{tabular}{l}
+    \verb"\documentclass[12pt]{amsart}"\\
+    \verb"\usepackage{amscd}"
+  \end{tabular}
+\end{center}
+which select the \verb"amsart" document class with twelve point type,
+and loads the macros for the \verb"CD" environment.
+
+\subsubsection*{A simple example}
+
+To produce the diagram
+$$
+\begin{CD}
+A    @>>>  B   @=     B\\
+@AAA       @|         @VVV\\
+X    @<<<  B   @>>>   Y
+\end{CD}
+$$
+you type
+\begin{verbatim}
+$$
+\begin{CD}
+A    @>>>  B   @=     B\\
+@AAA       @|         @VVV\\
+X    @<<<  B   @>>>   Y
+\end{CD}
+$$
+\end{verbatim}
+This illustrates several things.  First of all, the \verb"CD"
+environment must be inside of a displayed mathematics environment.
+(Here we used the standard \verb"$$" toggle to get displayed
+mathematics.  If we had used, e.g., \verb"\begin{equation}" and
+  \verb"\end{equation}", we would have had an equation number assigned
+to the display.)  Right pointing arrows are obtained with \verb"@>>>",
+left pointing arrows with \verb"@<<<", up pointing arrows with
+\verb"@AAA", down pointing arrows with \verb"@VVV", horizontal equals
+signs with \verb"@=", and vertical equals signs with \verb"@|".  Every
+line except the last is ended with a double backslash (\verb"\\").
+
+\subsubsection*{Labeling the arrows}
+
+The arrows can also be labeled.  For horizontal arrows, anything
+between the first and second inequality sign goes above the arrow,
+and anything between the second and third inequality sign goes below
+it.  For downward arrows, anything between the first and second
+\verb"V" goes to the left, and anything between the second and third
+goes to the right (and similarly for upward arrows).  Thus, if you
+type
+\begin{verbatim}
+\begin{displaymath}
+\begin{CD}
+\mathrm{H}_iX    @>f_*>>   \mathrm{H}_iY   @<g_*<\iso<    E_fA\\
+@V\phi VV                  @V\psi VV                 @AA\Omega A\\
+\pi_iQ  @>\alpha\beta\gamma>>  \pi_i(R,S)
+                   @<<\text{A long arrow}<   \prod_{k=1}^i H_kZ
+\end{CD}
+\end{displaymath}
+\end{verbatim}
+you'll get
+\begin{displaymath}
+\begin{CD}
+\mathrm{H}_iX  @>f_*>>  \mathrm{H}_iY   @<g_*<\iso<    E_fA\\
+@V\phi VV               @V\psi VV                @AA\Omega A\\
+\pi_iQ   @>\alpha\beta\gamma>>    \pi_i(R,S)
+                   @<<\text{A long arrow}<   \prod_{k=1}^i H_kZ
+\end{CD}
+\end{displaymath}
+
+
+\subsubsection*{Leaving out part of the rectangle}
+
+If you want to end a line in the diagram early (omitting the right
+end of that line), just type the double backslash.  If you want to
+leave out the \emph{beginning} of a line, you type ``\verb"@."''
+(the ``at'' sign followed by a period) to denote an invisible arrow. 
+(It's the arrows that are the column markers in the \verb"CD"
+environment.)  Thus, if you type
+\begin{verbatim}
+\begin{displaymath}
+\begin{CD}
+X\\
+@VfVV\\
+Y  @=     Y\\
+@.       @VVgV\\
+  @.     Z
+\end{CD}
+\end{displaymath}
+\end{verbatim}
+you'll get
+\begin{displaymath}
+\begin{CD}
+X\\
+@VfVV\\
+Y  @=     Y\\
+@.       @VVgV\\
+  @.     Z
+\end{CD}
+\end{displaymath}
+
+
+
+
+
+%---------------------------------------------------------------------
+%---------------------------------------------------------------------
+\section{Macro definitions, a.k.a.\ \texttt{newcommand}}
+\label{sec:definitions}
+
+
+\LaTeX{} allows you to use the same \verb"\def" command that you use
+in plain \TeX, but it's considered bad style.  Instead, \LaTeX{} has
+the \verb"\newcommand" and \verb"\renewcommand" commands, which do a
+little error checking for you.  In plain \TeX, you might use the
+command
+\begin{center}
+\verb"\def\tensor{\otimes}"
+\end{center}
+but in \LaTeX, the preferred form is
+\begin{center}
+\verb"\newcommand{\tensor}{\otimes}"
+\end{center}
+The advantage of this is that \LaTeX{} will check to see if there
+already is a command with the name \verb"\tensor", and give you an
+error message if there is.  If you know that there is a previous
+definition of \verb"\tensor" but you \emph{want} to override it,
+then you use the command
+\begin{center}
+\verb"\renewcommand{\tensor}{\otimes}"
+\end{center}
+
+
+If you want to use macros with replaceable parameters, the
+\verb"newcommand" command allows this.  For the equivalent of the
+plain \TeX{} command
+\begin{center}
+\verb"\def\pushout#1#2#3{#1\cup_{#2}#3}"
+\end{center}
+you use the \LaTeX{} command
+\begin{center}
+\verb"\newcommand{\pushout}[3]{#1\cup_{#2}#3}"
+\end{center}
+i.e., the command name is enclosed in braces, and the number of
+parameters is enclosed in square brackets.
+
+
+
+%---------------------------------------------------------------------
+%---------------------------------------------------------------------
+\section{Lists: \texttt{itemize, enumerate, and description}}
+
+There are three list making environments: \texttt{itemize},
+\texttt{enumerate}, and \texttt{description}.  The \texttt{itemize}
+environment just lists the items with a marker in front of each one. 
+If you type
+%
+\begin{verbatim}
+\begin{itemize}
+\item
+This is the first item in the list, which runs on long enough to
+spill over onto a second line.
+\item
+This is the second item in the list, which is a bit shorter.
+\item
+This is the last item.
+\end{itemize}
+\end{verbatim}
+%
+then you'll get
+%
+\begin{itemize}
+\item
+This is the first item in the list, which runs on long enough to
+spill over onto a second line.
+\item
+This is the second item in the list, which is a bit shorter.
+\item
+This is the last item.
+\end{itemize}
+
+
+
+The \texttt{enumerate} environment looks the same, except that the items
+in the list are numbered.  If you type
+\begin{verbatim}
+\begin{enumerate}
+\item
+This is the first item in the list, which runs on long enough to
+spill over onto a second line.
+\item
+This is the second item in the list, which is a bit shorter.
+\item
+This is the last item.
+\end{enumerate}
+\end{verbatim}
+then you'll get
+\begin{enumerate}
+\item
+This is the first item in the list, which runs on long enough to
+spill over onto a second line.
+\item
+This is the second item in the list, which is a bit shorter.
+\item
+This is the last item.
+\end{enumerate}
+
+The \texttt{description} environment requires an extra argument for each
+\verb"\item" command, which will be printed at the beginning of the
+item.  If you type
+\begin{verbatim}
+\begin{description}
+\item[sedge]
+A green plant, found in both wetlands and uplands.
+Sedges are often confused with grasses and rushes.
+\item[grass]
+A green plant, found in both wetlands and uplands.
+Grasses are often confused with sedges and rushes.
+\item[rush]
+A green plant, found in both wetlands and uplands.
+Rushes are often confused with sedges and grasses
+\end{description}
+\end{verbatim}
+you'll get
+\begin{description}
+\item[sedge]
+A green plant, found in both wetlands and uplands.  Sedges are often
+confused with grasses and rushes.
+\item[grass]
+A green plant, found in both wetlands and uplands.  Grasses are often
+confused with sedges and rushes.
+\item[rush]
+A green plant, found in both wetlands and uplands.  Rushes are often
+confused with sedges and grasses
+\end{description}
+
+
+These environments can be inserted within each other, and the
+\verb"enumerate" environment keeps track of what level it's at, and
+numbers its items accordingly.  If you type
+\begin{verbatim}
+\begin{enumerate}
+\item I went to the dry cleaners.
+\item I went to the supermarket.  I bought
+\begin{enumerate}
+\item Bread,
+\item cheese, and
+\item Tabasco sauce.
+\end{enumerate}
+\item I went to the bank.
+\end{enumerate}
+\end{verbatim}
+%
+you'll get
+%
+\begin{enumerate}
+\item I went to the dry cleaners.
+\item I went to the supermarket.  I bought
+\begin{enumerate}
+\item Bread,
+\item cheese, and
+\item Tabasco sauce.
+\end{enumerate}
+\item I went to the bank.
+\end{enumerate}
+
+
+
+
+
+
+
+
+%---------------------------------------------------------------------
+%---------------------------------------------------------------------
+\section{The bibliography}
+\label{sec:bibliography}
+
+\subsection{\texttt{begin\{thebibliography\}} and 
+  \texttt{end\{thebibliography\}}}
+
+
+The bibliography is begun with the command
+\begin{center}
+\verb"\begin{thebibliography}{number}"
+\end{center}
+where \emph{number} is a random number that, when printed, is as
+wide as the widest number of any item in the bibliography.  (The only
+use made of \verb"number" is that \LaTeX{} assumes that the numbers
+that it will assign to the actual items in the bibliography will be
+no wider (when printed) than \verb"number".) For example, if the
+bibliography will contain between 10 and~19 items, you can use
+\verb"\begin{thebibliography}{10}".
+
+After listing each item in the bibliography, you end the bibliography
+with the \verb"\end{thebibliography}" command.
+
+
+\subsection{Bibliography items}
+
+Each item is begun with a \verb"\bibitem" command.  The format is
+\begin{center}
+\verb"\bibitem{key for cross-references}Item entry"
+\end{center}
+For example, the bibliography in these instructions contains the
+entry
+%
+\begin{verbatim}
+\bibitem{yellowmonster}
+A. K. Bousfield and D. M. Kan, \emph{Homotopy Limits,
+Completions and Localizations,} Lecture Notes in
+Mathematics number 304, Springer-Verlag, New York, 1972.
+\end{verbatim}
+
+
+The above entry allows you to say
+\begin{verbatim}
+Homotopy inverse limits are discussed
+in~\cite[Chapter 11]{yellowmonster}.
+\end{verbatim}
+and have it print as
+``Homotopy inverse limits are discussed
+in~\cite[Chapter 11]{yellowmonster}.''
+For more on this, see Section~\ref{sec:bibreferences}.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+%---------------------------------------------------------------------
+%---------------------------------------------------------------------
+\section{The template file}
+\label{sec:template}
+
+The following is the text of the file \verb"template.tex".
+
+\begin{verbatim}
+%%% template.tex
+%%% This is a template for making up an AMS-LaTeX file
+%%% Version of August 10, 2000
+%%%---------------------------------------------------------
+%%% The following commands choose 12 point type (instead
+%%% of the default 10 point), allow us to use the
+%%% commutative diagram macros, and define the standard
+%%% names for all of the special symbols in the AMSfonts
+%%% package:
+\documentclass[12pt]{amsart}
+\usepackage{amscd}
+\usepackage{amssymb}
+
+
+
+
+
+%%% This part of the file (after the \documentclass command,
+%%% but before the \begin{document}) is called the ``preamble''.
+%%% This is a good place to  put our macro definitions.
+
+\newcommand{\tensor}{\otimes}
+\newcommand{\homotopic}{\simeq}
+\newcommand{\homeq}{\cong}
+\newcommand{\iso}{\approx}
+
+\DeclareMathOperator{\ho}{Ho}
+\DeclareMathOperator*{\colim}{colim}
+
+
+
+\newcommand{\R}{\mathbb{R}}
+\newcommand{\C}{\mathbb{C}}
+\newcommand{\Z}{\mathbb{Z}}
+
+\newcommand{\M}{\mathcal{M}}
+\newcommand{\W}{\mathcal{W}}
+
+
+
+\newcommand{\itilde}{\tilde{\imath}}
+\newcommand{\jtilde}{\tilde{\jmath}}
+\newcommand{\ihat}{\hat{\imath}}
+\newcommand{\jhat}{\hat{\jmath}}
+
+
+
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%% The Theorem environments:
+%%%
+%%%
+%%% The following commands set it up so that:
+%%% 
+%%% All Theorems, Corollaries, Lemmas, Propositions, Definitions,
+%%% Remarks, Examples, Notations, and Terminologies  will be numbered
+%%% in a single sequence, and the numbering will be within each
+%%% section.  Displayed equations will be numbered in the same
+%%% sequence. 
+%%% 
+%%% 
+%%% Theorems, Propositions, Lemmas, and Corollaries will have the most
+%%% formal typesetting.
+%%% 
+%%% Definitions will have the next level of formality.
+%%% 
+%%% Remarks, Examples, Notations, and Terminologies will be the least
+%%% formal.
+%%% 
+%%% Theorem:
+%%% \begin{thm}
+%%% 
+%%% \end{thm}
+%%% 
+%%% Corollary:
+%%% \begin{cor}
+%%% 
+%%% \end{cor}
+%%% 
+%%% Lemma:
+%%% \begin{lem}
+%%% 
+%%% \end{lem}
+%%% 
+%%% Proposition:
+%%% \begin{prop}
+%%% 
+%%% \end{prop}
+%%% 
+%%% Definition:
+%%% \begin{defn}
+%%% 
+%%% \end{defn}
+%%% 
+%%% Remark:
+%%% \begin{rem}
+%%% 
+%%% \end{rem}
+%%% 
+%%% Example:
+%%% \begin{ex}
+%%% 
+%%% \end{ex}
+%%% 
+%%% Notation:
+%%% \begin{notation}
+%%% 
+%%% \end{notation}
+%%% 
+%%% Terminology:
+%%% \begin{terminology}
+%%% 
+%%% \end{terminology}
+%%% 
+%%%       Theorem environments
+
+% The following causes equations to be numbered within sections
+\numberwithin{equation}{section}
+
+% We'll use the equation counter for all our theorem environments, so
+% that everything will be numbered in the same sequence.
+
+%       Theorem environments
+
+\theoremstyle{plain} %% This is the default, anyway
+\newtheorem{thm}[equation]{Theorem}
+\newtheorem{cor}[equation]{Corollary}
+\newtheorem{lem}[equation]{Lemma}
+\newtheorem{prop}[equation]{Proposition}
+
+
+\theoremstyle{definition}
+\newtheorem{defn}[equation]{Definition}
+
+\theoremstyle{remark}
+\newtheorem{rem}[equation]{Remark}
+\newtheorem{ex}[equation]{Example}
+\newtheorem{notation}[equation]{Notation}
+\newtheorem{terminology}[equation]{Terminology}
+
+
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+\begin{document}
+
+%%% In the title, use a double backslash "\\" to show a linebreak:
+%%% Use one of the following two forms:
+%%% \title{Text of the title}
+%%% or
+%%% \title[Short form for the running head]{Text of the title}
+\title
+
+
+
+
+\author{}
+
+
+
+%%% In the address, show linebreaks with double backslashes:
+\address{}
+
+
+
+
+%%% Email address is optional.
+\email{}
+
+%%% To have the current date inserted, use \date{\today}:
+\date{}
+
+
+\maketitle
+
+%%% To include a table of contents, uncomment the next line:
+% \tableofcontents
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%% Start the body of the paper here!  E.G., maybe use:
+%%% \section{Introduction}
+%%% \label{sec:intro}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%% The number "10" that appears in the next command is a TOTALLY
+%%% RANDOM NUMBER which is chosen so that if it was printed, it would
+%%% be at least as wide as any number of an item in the bibliography:
+
+\begin{thebibliography}{10}
+
+
+
+
+%%% The format of bibliography items is as in the following examples:
+%%% 
+%%% \bibitem{yellowmonster}
+%%% A. K. Bousfield and D. M. Kan, \emph{Homotopy Limits, Completions
+%%% and Localizations,} Lecture Notes in Mathematics number 304,
+%%% Springer-Verlag, New York, 1972.
+%%% 
+%%% \bibitem{HA}
+%%% D. G. Quillen, \emph{Homotopical Algebra,} Lecture Notes in
+%%% Mathematics number 43, Springer-Verlag, Berlin, 1967.
+
+
+
+
+
+
+
+
+\end{thebibliography}
+\end{document}
+\end{verbatim}
+
+
+
+
+
+
+
+
+
+
+
+%---------------------------------------------------------------------
+%---------------------------------------------------------------------
+
+\begin{thebibliography}{10}
+
+
+\bibitem{amslatexusersguide} 
+  American Mathematical Society, \emph{\AmS-\LaTeX{} Version 1.2 User's
+    Guide,} November, 1996.  This is the file \texttt{amsldoc.dvi},
+  available from the AMS ftp site \texttt{e-math.ams.org}.
+
+\bibitem{instr-l} 
+  American Mathematical Society, \emph{Instructions for preparation of
+    papers and monographs: \AmS-\LaTeX,} November, 1966.  This is the
+  file \texttt{instr-l.dvi}, available from the AMS ftp site
+  \texttt{e-math.ams.org}.
+
+\bibitem{testmath}
+  American Mathematical Society, \emph{Sample paper for the amsmath
+    package,} November, 1996.  This is the file \texttt{testmath.tex},
+  available from the AMS ftp site \texttt{e-math.ams.org}.
+
+\bibitem{latex}
+  Leslie Lamport, \emph{\LaTeX{} User's Guide and Reference Manual,}
+  Addison-Wesley, 1986.
+
+\bibitem{NotShort} 
+  Tobias Oetiker, Hubert Partl, Irene Hyna, and Elisabeth Schlegl
+  \emph{The not so short introduction to \LaTeXe}, available by ftp
+  from CTAN (the Comprehensive \TeX{} archive network), at
+  \verb"ftp.tex.ac.uk", \verb"ftp.dante.de", and many mirrors, under
+  the name \verb"lshort2e.tex" or \verb"lshort2e.dvi".
+
+\bibitem{yellowmonster}
+  A. K. Bousfield and D. M. Kan, \emph{Homotopy Limits, Completions
+    and Localizations,} Lecture Notes in Mathematics number 304,
+  Springer-Verlag, New York, 1972.
+
+\bibitem{HA}
+  D. G. Quillen, \emph{Homotopical Algebra,} Lecture Notes in
+  Mathematics number 43, Springer-Verlag, Berlin, 1967.
+
+
+\end{thebibliography}
+\end{document}
+
diff --git a/Master/texmf-dist/doc/latex/amslatex-primer/template.tex b/Master/texmf-dist/doc/latex/amslatex-primer/template.tex
new file mode 100644
index 00000000000..f536a095bb5
--- /dev/null
+++ b/Master/texmf-dist/doc/latex/amslatex-primer/template.tex
@@ -0,0 +1,234 @@
+%%% template.tex
+%%% This is a template for making up an AMS-LaTeX file
+%%% Version of August 10, 2000
+%%%---------------------------------------------------------
+%%% The following commands choose 12 point type (instead
+%%% of the default 10 point), allow us to use the
+%%% commutative diagram macros, and define the standard
+%%% names for all of the special symbols in the AMSfonts
+%%% package:
+\documentclass[12pt]{amsart}
+\usepackage{amscd}
+\usepackage{amssymb}
+
+
+
+
+
+%%% This part of the file (after the \documentclass command,
+%%% but before the \begin{document}) is called the ``preamble''.
+%%% This is a good place to  put our macro definitions.
+
+\newcommand{\tensor}{\otimes}
+\newcommand{\homotopic}{\simeq}
+\newcommand{\homeq}{\cong}
+\newcommand{\iso}{\approx}
+
+\DeclareMathOperator{\ho}{Ho}
+\DeclareMathOperator*{\colim}{colim}
+
+
+
+\newcommand{\R}{\mathbb{R}}
+\newcommand{\C}{\mathbb{C}}
+\newcommand{\Z}{\mathbb{Z}}
+
+\newcommand{\M}{\mathcal{M}}
+\newcommand{\W}{\mathcal{W}}
+
+
+
+\newcommand{\itilde}{\tilde{\imath}}
+\newcommand{\jtilde}{\tilde{\jmath}}
+\newcommand{\ihat}{\hat{\imath}}
+\newcommand{\jhat}{\hat{\jmath}}
+
+
+
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%% The Theorem environments:
+%%%
+%%%
+%%% The following commands set it up so that:
+%%% 
+%%% All Theorems, Corollaries, Lemmas, Propositions, Definitions,
+%%% Remarks, Examples, Notations, and Terminologies  will be numbered
+%%% in a single sequence, and the numbering will be within each
+%%% section.  Displayed equations will be numbered in the same
+%%% sequence. 
+%%% 
+%%% 
+%%% Theorems, Propositions, Lemmas, and Corollaries will have the most
+%%% formal typesetting.
+%%% 
+%%% Definitions will have the next level of formality.
+%%% 
+%%% Remarks, Examples, Notations, and Terminologies will be the least
+%%% formal.
+%%% 
+%%% Theorem:
+%%% \begin{thm}
+%%% 
+%%% \end{thm}
+%%% 
+%%% Corollary:
+%%% \begin{cor}
+%%% 
+%%% \end{cor}
+%%% 
+%%% Lemma:
+%%% \begin{lem}
+%%% 
+%%% \end{lem}
+%%% 
+%%% Proposition:
+%%% \begin{prop}
+%%% 
+%%% \end{prop}
+%%% 
+%%% Definition:
+%%% \begin{defn}
+%%% 
+%%% \end{defn}
+%%% 
+%%% Remark:
+%%% \begin{rem}
+%%% 
+%%% \end{rem}
+%%% 
+%%% Example:
+%%% \begin{ex}
+%%% 
+%%% \end{ex}
+%%% 
+%%% Notation:
+%%% \begin{notation}
+%%% 
+%%% \end{notation}
+%%% 
+%%% Terminology:
+%%% \begin{terminology}
+%%% 
+%%% \end{terminology}
+%%% 
+%%%       Theorem environments
+
+% The following causes equations to be numbered within sections
+\numberwithin{equation}{section}
+
+% We'll use the equation counter for all our theorem environments, so
+% that everything will be numbered in the same sequence.
+
+%       Theorem environments
+
+\theoremstyle{plain} %% This is the default, anyway
+\newtheorem{thm}[equation]{Theorem}
+\newtheorem{cor}[equation]{Corollary}
+\newtheorem{lem}[equation]{Lemma}
+\newtheorem{prop}[equation]{Proposition}
+
+
+\theoremstyle{definition}
+\newtheorem{defn}[equation]{Definition}
+
+\theoremstyle{remark}
+\newtheorem{rem}[equation]{Remark}
+\newtheorem{ex}[equation]{Example}
+\newtheorem{notation}[equation]{Notation}
+\newtheorem{terminology}[equation]{Terminology}
+
+
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+\begin{document}
+
+%%% In the title, use a double backslash "\\" to show a linebreak:
+%%% Use one of the following two forms:
+%%% \title{Text of the title}
+%%% or
+%%% \title[Short form for the running head]{Text of the title}
+\title
+
+
+
+
+\author{}
+
+
+
+%%% In the address, show linebreaks with double backslashes:
+\address{}
+
+
+
+
+%%% Email address is optional.
+\email{}
+
+%%% To have the current date inserted, use \date{\today}:
+\date{}
+
+
+\maketitle
+
+%%% To include a table of contents, uncomment the next line:
+% \tableofcontents
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%% Start the body of the paper here!  E.G., maybe use:
+%%% \section{Introduction}
+%%% \label{sec:intro}
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%% The number "10" that appears in the next command is a TOTALLY
+%%% RANDOM NUMBER which is chosen so that if it was printed, it would
+%%% be at least as wide as any number of an item in the bibliography:
+
+\begin{thebibliography}{10}
+
+
+
+
+%%% The format of bibliography items is as in the following examples:
+%%% 
+%%% \bibitem{yellowmonster}
+%%% A. K. Bousfield and D. M. Kan, \emph{Homotopy Limits, Completions
+%%% and Localizations,} Lecture Notes in Mathematics number 304,
+%%% Springer-Verlag, New York, 1972.
+%%% 
+%%% \bibitem{HA}
+%%% D. G. Quillen, \emph{Homotopical Algebra,} Lecture Notes in
+%%% Mathematics number 43, Springer-Verlag, Berlin, 1967.
+
+
+
+
+
+
+
+
+\end{thebibliography}
+\end{document}