%%% 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}