%%% 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}