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+%%% template.tex
+%%% This is a template for making up an AMS-LaTeX file
+%%% Version of December 16, 1992
+%%%------------------------------------------------------------------
+%%% The following documentstyle command chooses 12 point type (instead
+%%% of the default 10 point), allows us to use the commutative
+%%% diagram macros, and defines the standard names for all of the
+%%% special symbols in the AMSfonts package:
+\documentstyle[12pt,amscd,amssymb]{amsart}
+
+
+
+
+
+
+%%% This part of the file (after the documentstyle 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}
+\newcommand{\ho}{\operatorname{Ho}}
+
+% Homotopy direct limit:
+\newcommand{\hodlim}{\underrightarrow
+{\operatorname{\mathstrut holim}}}
+
+% Homotopy inverse limit:
+\newcommand{\hoilim}{\underleftarrow
+{\operatorname{\mathstrut holim}}}
+
+
+
+
+
+\newcommand{\C}{{\cal C}}
+\newcommand{\M}{{\cal M}}
+\newcommand{\W}{{\cal W}}
+
+
+
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%% The Theorem environments:
+%%%
+%%%
+%%% The following commands set it up so that:
+%%%
+%%% All Theorems, Corollaries, Lemmas, Propositions, Definitions,
+%%% Remarks, and Examples will be numbered in a single sequence, and
+%%% the numbering will be within each section.
+%%%
+%%% Anything called `bigthm' in the TeXfile will be printed as
+%%% Theorem, but will be numbered in a separate sequence, named
+%%% Theorem A, Theorem B, Theorem C, etc.
+%%%
+%%%
+%%% Notations and Terminologies will not be numbered.
+%%%
+%%% 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}
+%%%
+%%% Theorem: (Numbered separately, as Theorem A, etc.)
+%%% \begin{bigthm}
+%%%
+%%% \end{bigthm}
+%%%
+%%% 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
+
+\theoremstyle{plain} %% This is the default, anyway
+\begingroup % Confine the \theorembodyfont command
+\theorembodyfont{\sl}
+\newtheorem{bigthm}{Theorem} % Numbered separately, as A, B, etc.
+\newtheorem{thm}{Theorem}[section] % Numbered within each section
+\newtheorem{cor}[thm]{Corollary} % Numbered along with thm
+\newtheorem{lem}[thm]{Lemma} % Numbered along with thm
+\newtheorem{prop}[thm]{Proposition} % Numbered along with thm
+\endgroup
+
+%%% We need to do the following outside of any group,
+%%% since it's not \global:
+\renewcommand{\thebigthm}{\Alph{bigthm}} % Number as "Theorem A."
+
+
+\theoremstyle{definition}
+\newtheorem{defn}[thm]{Definition} % Numbered along with thm
+
+\theoremstyle{remark}
+\newtheorem{rem}[thm]{Remark} % Numbered along with thm
+\newtheorem{ex}[thm]{Example} % Numbered along with thm
+\newtheorem{notation}{Notation}
+\renewcommand{\thenotation}{} % to make the notation
+ % environment unnumbered
+\newtheorem{terminology}{Terminology}
+\renewcommand{\theterminology}{} % to make the terminology
+ % environment unnumbered
+%%%-------------------------------------------------------------------
+%%% The following causes equations to be numbered within sections:
+\numberwithin{equation}{section}
+
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+%%%-------------------------------------------------------------------
+\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. If you include it, use a double at
+%%% sign "@@" to produce a single at sign in the printed copy, e.g.,
+%%% \email{nsteenrod@@math.princeton.edu}
+\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, {\em Homotopy Limits, Completions
+%%% and Localizations,} Lecture Notes in Mathematics number 304,
+%%% Springer-Verlag, New York, 1972.
+%%%
+%%% \bibitem{HA}
+%%% D. G. Quillen, {\em Homotopical Algebra,} Lecture Notes in
+%%% Mathematics number 43, Springer-Verlag, Berlin, 1967.
+
+
+
+
+
+
+
+
+\end{thebibliography}
+\end{document}