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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}