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+%%% 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}