%% %% This is file `nchairx.sty', %% generated with the docstrip utility. %% %% The original source files were: %% %% nchairx.dtx (with options: `nchairx') %% chairxDefaults.dtx (with options: `chairxDefaults') %% chairxEnv.dtx (with options: `chairxEnv') %% chairxLogo.dtx (with options: `chairxLogo') %% chairxmathFonts.dtx (with options: `chairxmathFonts') %% chairxmathDelimiters.dtx (with options: `chairxmathDelimiters') %% chairxmathDecoration.dtx (with options: `chairxmathDecoration') %% chairxmathGeneral.dtx (with options: `chairxmathGeneral') %% chairxmathAlgebra.dtx (with options: `chairxmathAlgebra') %% chairxmathAnalysis.dtx (with options: `chairxmathAnalysis') %% chairxmathCategory.dtx (with options: `chairxmathCategory') %% chairxmathDiffgeo.dtx (with options: `chairxmathDiffgeo') %% chairxmathLinalg.dtx (with options: `chairxmathLinalg') %% chairxmathStatistics.dtx (with options: `chairxmathStatistics') %% chairxmathTopology.dtx (with options: `chairxmathTopology') %% This is a generated file. %% %% Copyright (C) 2018 by ChairX %% %% This file may be distributed and/or modified under the %% conditions of the LaTeX Project Public License, either %% version 1.3 of this license or (at your option) any later %% version. The latest version of this license is in: %% %% http://www.latex-project.org/lppl.txt %% and version 1.3 or later is part of all distributions of %% %% LaTeX version 2005/12/01 or later. % This work may be distributed and/or modified under the \NeedsTeXFormat{LaTeX2e} \ProvidesPackage{nchairx} [2021/07/29 v1.0.0 First major release] \RequirePackage{xkeyval} \newif\if@loadmath \@loadmathtrue \DeclareOptionX[chairx]{noMath}{ \@loadmathfalse } \ProcessOptionsX[chairx] \RequirePackage{amsmath} \RequirePackage{amssymb} \RequirePackage{suffix} \RequirePackage{mathtools} \RequirePackage[amsmath,thmmarks,hyperref]{ntheorem} \RequirePackage{graphicx} \RequirePackage{enumitem} \RequirePackage{tensor} \DeclareSymbolFont{stmry}{U}{stmry}{m}{n} \SetSymbolFont{stmry}{bold}{U}{stmry}{b}{n} \RequirePackage{aliascnt} \numberwithin{equation}{section} \renewcommand{\theequation}{\thesection.\arabic{equation}} \allowdisplaybreaks \renewcommand{\arraystretch}{1.2} \let\originalleft\left \let\originalright\right \renewcommand{\left}{\mathopen{}\mathclose\bgroup\originalleft} \renewcommand{\right}{\aftergroup\egroup\originalright} \renewcommand{\cleardoublepage}{\clearpage\ifodd\c@page\else\vspace*{\fill}\thispagestyle{empty}\newpage\fi} \newcommand{\claimch@irxname}{Claim} \newcommand{\conjecturech@irxname}{Conjecture} \newcommand{\conventionch@irxname}{Convention} \newcommand{\corollarych@irxname}{Corollary} \newcommand{\definitionch@irxname}{Definition} \newcommand{\examplech@irxname}{Example} \newcommand{\exercisech@irxname}{Exercise} \newcommand{\hintch@irxname}{Hint} \newcommand{\lemmach@irxname}{Lemma} \newcommand{\maintheoremch@irxname}{Main Theorem} \newcommand{\notationch@irxname}{Notation} \newcommand{\proofch@irxname}{Proof} \newcommand{\propositionch@irxname}{Proposition} \newcommand{\questionch@irxname}{Question} \newcommand{\remarkch@irxname}{Remark} \newcommand{\subproofch@irxname}{Proof} \newcommand{\theoremch@irxname}{Theorem} \@ifpackagewith{babel}{english,strings}{% \StartBabelCommands{english}{extras} \SetString{\chapterch@irxname}{Chapter} \SetString{\sectionch@irxname}{Section} \SetString{\subsectionch@irxname}{Section} \SetString{\subsubsectionch@irxname}{Section} \SetString{\lemmach@irxname}{Lemma} \SetString{\propositionch@irxname}{Proposition} \SetString{\theoremch@irxname}{Theorem} \SetString{\corollarych@irxname}{Corollary} \SetString{\definitionch@irxname}{Definition} \SetString{\claimch@irxname}{Claim} \SetString{\examplech@irxname}{Example} \SetString{\remarkch@irxname}{Remark} \SetString{\questionch@irxname}{Question} \SetString{\conjecturech@irxname}{Conjecture} \SetString{\conventionch@irxname}{Convention} \SetString{\exercisech@irxname}{Exercise} \SetString{\maintheoremch@irxname}{Main Theorem} \SetString{\notationch@irxname}{Notation} \SetString{\proofch@irxname}{Proof} \SetString{\subproofch@irxname}{Proof} \SetString{\hintch@irxname}{Hint} \EndBabelCommands }{} \@ifpackagewith{babel}{german,strings}{% \StartBabelCommands{german}{extras} \SetString{\chapterch@irxname}{Kapitel} \SetString{\sectionch@irxname}{Abschnitt} \SetString{\subsectionch@irxname}{Abschnitt} \SetString{\subsubsectionch@irxname}{Abschnitt} \SetString{\lemmach@irxname}{Lemma} \SetString{\propositionch@irxname}{Proposition} \SetString{\theoremch@irxname}{Satz} \SetString{\corollarych@irxname}{Korollar} \SetString{\definitionch@irxname}{Definition} \SetString{\claimch@irxname}{Behauptung} \SetString{\examplech@irxname}{Beispiel} \SetString{\remarkch@irxname}{Bemerkung} \SetString{\questionch@irxname}{Frage} \SetString{\conjecturech@irxname}{Vermutung} \SetString{\conventionch@irxname}{Konvention} \SetString{\exercisech@irxname}{\"Ubung} \SetString{\maintheoremch@irxname}{Theorem} \SetString{\notationch@irxname}{Notation} \SetString{\proofch@irxname}{Beweis} \SetString{\subproofch@irxname}{Beweis} \SetString{\hintch@irxname}{Hinweis} \EndBabelCommands }{} \theoremheaderfont{\normalfont\bfseries} \theorembodyfont{\itshape} \newtheorem{claim}{\claimch@irxname}[section] \newtheorem*{nnclaim}{\claimch@irxname} \newaliascnt{conjecture}{claim} \newtheorem{conjecture}[conjecture]{\conjecturech@irxname} \newtheorem*{nnconjecture}{\conjecturech@irxname} \aliascntresetthe{conjecture} \newaliascnt{corollary}{claim} \newtheorem{corollary}[corollary]{\corollarych@irxname} \newtheorem*{nncorollary}{\corollarych@irxname} \aliascntresetthe{corollary} \newaliascnt{definition}{claim} \newtheorem{definition}[definition]{\definitionch@irxname} \newtheorem*{nndefinition}{\definitionch@irxname} \aliascntresetthe{definition} \newaliascnt{lemma}{claim} \newtheorem{lemma}[lemma]{\lemmach@irxname} \newtheorem*{nnlemma}{\lemmach@irxname} \aliascntresetthe{lemma} \newaliascnt{proposition}{claim} \newtheorem{proposition}[proposition]{\propositionch@irxname} \newtheorem*{nnproposition}{\propositionch@irxname} \aliascntresetthe{proposition} \newaliascnt{theorem}{claim} \newtheorem{theorem}[theorem]{\theoremch@irxname} \newtheorem*{nntheorem}{\theoremch@irxname} \aliascntresetthe{theorem} \theorembodyfont{\rmfamily} \newaliascnt{example}{claim} \newtheorem{example}[example]{\examplech@irxname} \newtheorem*{nnexample}{\examplech@irxname} \aliascntresetthe{example} \newaliascnt{convention}{claim} \newtheorem{convention}[convention]{\conventionch@irxname} \newtheorem*{nnconvention}{\conventionch@irxname} \aliascntresetthe{convention} \newaliascnt{notation}{claim} \newtheorem{notation}[notation]{\notationch@irxname} \newtheorem*{nnnotation}{\notationch@irxname} \aliascntresetthe{notation} \newaliascnt{question}{claim} \newtheorem{question}[question]{\questionch@irxname} \newtheorem*{nnquestion}{\questionch@irxname} \aliascntresetthe{question} \newaliascnt{remark}{claim} \newtheorem{remark}[remark]{\remarkch@irxname} \newtheorem*{nnremark}{\remarkch@irxname} \aliascntresetthe{remark} \newtheorem{exercise}{\exercisech@irxname}[section] \newtheorem*{nnexercise}{\exercisech@irxname} \theorembodyfont{\itshape} \theoremnumbering{Roman} \newtheorem{maintheorem}{\maintheoremch@irxname} \newtheorem*{nnmaintheorem}{\maintheoremch@irxname} \DeclareMathSymbol\ch@irxboxempty{\mathord}{AMSa}{"03} \theoremheaderfont{\scshape} \theorembodyfont{\normalfont} \theoremstyle{nonumberplain} \theoremseparator{:} \theoremsymbol{\hbox{$\ch@irxboxempty$}} \newtheorem{proof}{\proofch@irxname} \theoremsymbol{\hbox{$\triangledown$}} \newtheorem{subproof}{\proofch@irxname} \newenvironment{hint}{\par\footnotesize\medskip\noindent\hintch@irxname: }{\par\smallskip\normalsize} \def\theorem@checkbold{} \providecommand{\claimautorefname}{\claimch@irxname} \providecommand{\conjectureautorefname}{\conjecturech@irxname} \providecommand{\conventionautorefname}{\conventionch@irxname} \providecommand{\corollaryautorefname}{\corollarych@irxname} \providecommand{\definitionautorefname}{\definitionch@irxname} \providecommand{\lemmaautorefname}{\lemmach@irxname} \providecommand{\propositionautorefname}{\propositionch@irxname} \providecommand{\exampleautorefname}{\examplech@irxname} \providecommand{\notationautorefname}{\notationch@irxname} \providecommand{\questionautorefname}{\questionch@irxname} \providecommand{\remarkautorefname}{\remarkch@irxname} \providecommand{\exerciseautorefname}{\exercisech@irxname} \providecommand{\thmautorefname}{\theoremch@irxname} \providecommand{\maintheoremautorefname}{\maintheoremch@irxname} \AtBeginDocument{ \@ifpackagewith{babel}{english,strings}{% \StartBabelCommands{english}{extras} \SetString{\chapterautorefname}{\chapterch@irxname} \SetString{\sectionautorefname}{\sectionch@irxname} \SetString{\subsectionautorefname}{\subsectionch@irxname} \SetString{\subsubsectionautorefname}{\subsubsectionch@irxname} \SetString{\theoremautorefname}{\theoremch@irxname} \EndBabelCommands }{} \@ifpackagewith{babel}{german,strings}{% \StartBabelCommands{german}{extras} \SetString{\chapterautorefname}{\chapterch@irxname} \SetString{\sectionautorefname}{\sectionch@irxname} \SetString{\subsectionautorefname}{\subsectionch@irxname} \SetString{\subsubsectionautorefname}{\subsubsectionch@irxname} \SetString{\theoremautorefname}{\theoremch@irxname} \EndBabelCommands }{} } \newenvironment{claimlist}[1][]{% \enumerate[% topsep = 0.2em, partopsep = 0em, itemsep = 0.2em, parsep = 0.1em, label=\textit{\roman*.)}, #1% ]% }% {\endenumerate} \newenvironment{conjecturelist}[1][]{% \enumerate[% topsep = 0.2em, partopsep = 0em, itemsep = 0.2em, parsep = 0.1em, label=\textit{\roman*.)}, #1% ]% }% {\endenumerate} \newenvironment{conventionlist}[1][]{% \enumerate[% topsep = 0.2em, partopsep = 0em, itemsep = 0.2em, parsep = 0.1em, label=\textit{\roman*.)}, #1% ]% }% {\endenumerate} \newenvironment{corollarylist}[1][]{% \enumerate[% topsep = 0.2em, partopsep = 0em, itemsep = 0.2em, parsep = 0.1em, label=\textit{\roman*.)}, #1% ] }% {\endenumerate} \newenvironment{definitionlist}[1][]{% \enumerate[% topsep = 0.2em, partopsep = 0em, itemsep = 0.2em, parsep = 0.1em, label=\textit{\roman*.)}, #1% ] }% {\endenumerate} \newenvironment{lemmalist}[1][]{% \enumerate[% topsep = 0.2em, partopsep = 0em, itemsep = 0.2em, parsep = 0.1em, label=\textit{\roman*.)}, #1% ] }% {\endenumerate} \newenvironment{propositionlist}[1][]{% \enumerate[% topsep = 0.2em, partopsep = 0em, itemsep = 0.2em, parsep = 0.1em, label=\textit{\roman*.)}, #1% ] }% {\endenumerate} \newenvironment{theoremlist}[1][]{% \enumerate[% topsep = 0.2em, partopsep = 0em, itemsep = 0.2em, parsep = 0.1em, label=\textit{\roman*.)}, #1% ] }% {\endenumerate} \newenvironment{prooflist}[1][]{% \enumerate[% topsep = 0.2em, partopsep = 0em, itemsep = 0.2em, parsep = 0.1em, label=\textit{\roman*.)}, #1% ] }% {\endenumerate} \newenvironment{examplelist}[1][]{% \enumerate[% topsep = 0.2em, partopsep = 0em, itemsep = 0.2em, parsep = 0.1em, label=\textit{\roman*.)}, #1% ]% }% {\endenumerate} \newenvironment{notationlist}[1][]{% \enumerate[% topsep = 0.2em, partopsep = 0em, itemsep = 0.2em, parsep = 0.1em, label=\textit{\roman*.)}, #1% ]% }% {\enumerate} \newenvironment{questionlist}[1][]{% \enumerate[% topsep = 0.2em, partopsep = 0em, itemsep = 0.2em, parsep = 0.1em, label=\textit{\roman*.)}, #1% ]% }% {\endenumerate} \newenvironment{remarklist}[1][]{% \enumerate[% topsep = 0.2em, partopsep = 0em, itemsep = 0.2em, parsep = 0.1em, label=\textit{\roman*.)}, #1% ]% }% {\endenumerate} \newenvironment{exerciselist}[1][]{% \enumerate[% topsep = 0.2em, partopsep = 0em, itemsep = 0.2em, parsep = 0.1em, label=\textit{\roman*.)}, #1% ]% }% {\endenumerate} \newenvironment{maintheoremlist}[1][]{% \enumerate[% topsep = 0.2em, partopsep = 0em, itemsep = 0.2em, parsep = 0.1em, label=\textit{\roman*.)}, #1% ]% }% {\endenumerate} \newenvironment{cptenum}[1][]{% \enumerate[% topsep = 0.2em, partopsep = 0em, itemsep = 0.2em, parsep = 0.1em, label=\textit{\roman*.)}, #1% ] }% {\endenumerate} \newenvironment{cptitem}[1][]{% \begin{itemize}[% topsep = 0.2em, partopsep = 0em, itemsep = 0.2em, parsep = 0.1em, #1% ] }% {\end{itemize}} \newenvironment{cptdesc}[1][]{% \begin{description}[% topsep = 0.2em, partopsep = 0em, itemsep = 0.2em, parsep = 0.1em, #1% ] }% {\end{description}} \newcommand{\nchairxheader}{\includegraphics[width=\textwidth]{nchairxheader.pdf}} \newcommand{\nchairxlogo}[1]{\includegraphics[width=#1]{nchairxlogo.pdf}} \if@loadmath \DeclareMathAlphabet{\ch@airxmathbbm}{U}{bbm}{m}{n} \SetMathAlphabet\ch@airxmathbbm{bold}{U}{bbm}{bx}{n} \renewcommand{\mathbb}[1]{\ch@airxmathbbm{#1}} \DeclareMathAlphabet{\mathscr}{U}{rsfso}{m}{n} \DeclareSymbolFont{EulerScript}{U}{eus}{m}{n} \SetSymbolFont{EulerScript}{bold}{U}{eus}{b}{n} \DeclareSymbolFontAlphabet\mathcal{EulerScript} \define@key[chairx]{fonts}{algebrafont}{ \providecommand{\ch@irxalgebrafont}[1]{ } \renewcommand{\ch@irxalgebrafont}{#1} } \define@key[chairx]{fonts}{basisfont}{ \providecommand{\ch@irxbasisfont}[1]{ } \renewcommand{\ch@irxbasisfont}{#1} } \define@key[chairx]{fonts}{categoryfont}{ \providecommand{\ch@irxcategoryfont}[1]{ } \renewcommand{\ch@irxcategoryfont}{#1} } \define@key[chairx]{fonts}{categorynamefont}{ \providecommand{\ch@irxcategorynamefont}[1]{ } \renewcommand{\ch@irxcategorynamefont}{#1} } \define@key[chairx]{fonts}{fieldfont}{ \providecommand{\ch@irxfieldfont}[1]{ } \renewcommand{\ch@irxfieldfont}{#1} } \define@key[chairx]{fonts}{filterfont}{ \providecommand{\ch@irxfilterfont}[1]{ } \renewcommand{\ch@irxfilterfont}{#1} } \define@key[chairx]{fonts}{functorfont}{ \providecommand{\ch@irxfunctorfont}[1]{ } \renewcommand{\ch@irxfunctorfont}{#1} } \define@key[chairx]{fonts}{gerstenhaberfont}{ \providecommand{\ch@irxgerstenhaberfont}[1]{ } \renewcommand{\ch@irxgerstenhaberfont}{#1} } \define@key[chairx]{fonts}{groupfont}{ \providecommand{\ch@irxgroupfont}[1]{ } \renewcommand{\ch@irxgroupfont}{#1} } \define@key[chairx]{fonts}{groupoidfont}{ \providecommand{\ch@irxgroupoidfont}[1]{ } \renewcommand{\ch@irxgroupoidfont}{#1} } \define@key[chairx]{fonts}{hilbertfont}{ \providecommand{\ch@irxhilbertfont}[1]{ } \renewcommand{\ch@irxhilbertfont}{#1} } \define@key[chairx]{fonts}{liealgfont}{ \providecommand{\ch@irxliealgfont}[1]{ } \renewcommand{\ch@irxliealgfont}{#1} } \define@key[chairx]{fonts}{modulefont}{ \providecommand{\ch@irxmodulefont}[1]{ } \renewcommand{\ch@irxmodulefont}{#1} } \define@key[chairx]{fonts}{prehilbfont}{ \providecommand{\ch@irxprehilbfont}[1]{ } \renewcommand{\ch@irxprehilbfont}{#1} } \define@key[chairx]{fonts}{operatorfont}{ \providecommand{\ch@irxoperatorfont}[1]{ } \renewcommand{\ch@irxoperatorfont}{#1} } \define@key[chairx]{fonts}{ringfont}{ \providecommand{\ch@irxringfont}[1]{ } \renewcommand{\ch@irxringfont}{#1} } \define@key[chairx]{fonts}{scriptfont}{ \providecommand{\ch@irxscriptfont}[1]{ } \renewcommand{\ch@irxscriptfont}{#1} } \define@key[chairx]{fonts}{sheaffont}{ \providecommand{\ch@irxsheaffont}[1]{ } \renewcommand{\ch@irxsheaffont}{#1} } \define@key[chairx]{fonts}{spacefont}{ \providecommand{\ch@irxspacefont}[1]{ } \renewcommand{\ch@irxspacefont}{#1} } \define@key[chairx]{fonts}{topologyfont}{ \providecommand{\ch@irxtopologyfont}[1]{ } \renewcommand{\ch@irxtopologyfont}{#1} } \newcommand{\chairxfonts}[1]{ \setkeys[chairx]{fonts}{#1} } \chairxfonts{ algebrafont = \mathscr, basisfont = \mathit, categoryfont = \mathfrak, categorynamefont = \mathsf, fieldfont = \mathbb, filterfont = \mathfrak, functorfont = \mathsf, groupfont = \mathrm, groupoidfont = \mathfrak, gerstenhaberfont = \mathfrak, hilbertfont = \mathfrak, liealgfont = \mathfrak, modulefont = \mathscr, prehilbfont = \mathcal, operatorfont = \mathrm, ringfont = \mathsf, scriptfont = \mathrm, sheaffont = \mathscr, spacefont = \mathscr, topologyfont = \mathscr } \newcommand{\ch@irxfont}[1]{\fontfamily{#1}\fontencoding{U}\fontseries{m}\fontshape{n}\selectfont} \newcommand{\ch@irxsymbol}[2]{{\ch@irxfont{#1}\char#2}} \newcommand\ch@irxmathsymbol[3][\mathord]{% #1{\ch@irxm@thsymbol{#2}{#3}}} \def\ch@irxm@thsymbol#1#2{\mathchoice {\@ch@irxm@thsymbol{#1}{#2}\tf@size} {\@ch@irxm@thsymbol{#1}{#2}\tf@size} {\@ch@irxm@thsymbol{#1}{#2}\sf@size} {\@ch@irxm@thsymbol{#1}{#2}\ssf@size}} \def\@ch@irxm@thsymbol#1#2#3{\mbox{\fontsize{#3}{#3}\ch@irxsymbol{#1}{#2}}} \fi \if@loadmath \newcommand{\vast}{\bBigg@{4}} \newcommand{\Vast}{\bBigg@{5}} \newcommand{\vastl}{\mathopen\vast} \newcommand{\vastm}{\mathrel\vast} \newcommand{\vastr}{\mathclose\vast} \newcommand{\Vastl}{\mathopen\Vast} \newcommand{\Vastm}{\mathrel\Vast} \newcommand{\Vastr}{\mathclose\Vast} \fi \if@loadmath \let\originaltensor\tensor \DeclareRobustCommand\decorate{\originaltensor} \newcommand{\deco}[5]{\decorate*[^{#1}_{#2}]{#3}{^{#4}_{#5}}} \newcommand{\script}[1]{\ch@irxscriptfont{#1}} \fi \if@loadmath \newcommand{\I}{\mathrm{i}} \newcommand{\E}{\mathrm{e}} \newcommand{\D}{\mathop{}\!\mathrm{d}} \newcommand{\cc}[1]{\overline{{#1}}} \newcommand{\sign}{\operatorname{\ch@irxoperatorfont{sign}}} \newcommand{\RE}{\operatorname{\ch@irxoperatorfont{Re}}} \newcommand{\IM}{\operatorname{\ch@irxoperatorfont{Im}}} \newcommand{\Unit}{\mathbb{1}} \newcommand{\const}{\operatorname{\mathit{const}}} \newcommand{\canonical}{\ch@irxscriptfont{can}} \newcommand{\pt}{\ch@irxoperatorfont{pt}} \newcommand{\at}[2][\big]{#1\vert_{#2}} \newcommand{\Map}{\ch@irxoperatorfont{Map}} \newcommand{\Bij}{\ch@irxoperatorfont{Bij}} \newcommand{\argument}{\,\cdot\,} \newcommand{\domain}{\operatorname{\ch@irxoperatorfont{dom}}} \newcommand{\range}{\operatorname{\ch@irxoperatorfont{range}}} \newcommand{\id}{\operatorname{\ch@irxoperatorfont{id}}} \newcommand{\pr}{\operatorname{\ch@irxoperatorfont{pr}}} \newcommand{\inv}{\operatorname{\ch@irxoperatorfont{inv}}} \newcommand{\ev}{\operatorname{\ch@irxoperatorfont{ev}}} \newcommand{\image}{\operatorname{\ch@irxoperatorfont{im}}} \newcommand{\graph}{\operatorname{\ch@irxoperatorfont{graph}}} \newcommand{\coimage}{\operatorname{\ch@irxoperatorfont{coim}}} \newcommand{\coker}{\operatorname{\ch@irxoperatorfont{coker}}} \newcommand{\operator}[1]{\operatorname{\ch@irxoperatorfont{#1}}} \newcommand{\later}{\mathrel{\succcurlyeq}} \newcommand{\earlier}{\mathrel{\preccurlyeq}} \DeclareRobustCommand\big@p[2][1]{% \mathop{\vphantom{\sum}\mathpalette\bigop@{{#1}{#2}}}\slimits@ } \newcommand{\bigop@}[2]{\bigop@@#1#2} \newcommand{\bigop@@}[3]{% \vcenter{ \sbox\z@{$#1\sum$} \hbox{\resizebox{\ifx#1\displaystyle#2\fi\dimexpr\ht\z@+\dp\z@}{!}{$\m@th#3$}} } } \newcommand{\bigplus}{\DOTSB\big@p{+}} \newcommand{\bigtimes}{\DOTSB\big@p{\times}} \newcommand{\biprod}{\DOTSB\big@p{\mathrel{\prod\hspace{-0.4cm}\coprod}}} \newcommand{\smiley}{\ch@irxmathsymbol[\mathord]{wasy}{44}} \newcommand{\frownie}{\ch@irxmathsymbol[\mathord]{wasy}{47}} \newcommand{\heart}{\heartsuit} \fi \if@loadmath \newcommand{\field}[1]{\ch@irxfieldfont{#1}} \newcommand{\ring}[1]{\ch@irxringfont{#1}} \newcommand{\group}[1]{\ch@irxgroupfont{#1}} \newcommand{\algebra}[1]{\ch@irxalgebrafont{#1}} \newcommand{\module}[1]{\ch@irxmodulefont{#1}} \newcommand{\liealg}[1]{\ch@irxliealgfont{#1}} \newcommand{\MC}{{\scriptscriptstyle\ch@irxscriptfont{MC}}} \newcommand{\gerstenhaber}[1] {\ch@irxgerstenhaberfont{#1}} \newcommand{\Pol}{\ch@irxoperatorfont{Pol}} \newcommand{\lmult}{\operatorname{\ch@irxoperatorfont{\ell}}} \newcommand{\rmult}{\operatorname{\ch@irxoperatorfont{r}}} \newcommand{\Lmult}{\operatorname{\ch@irxoperatorfont{L}}} \newcommand{\Rmult}{\operatorname{\ch@irxoperatorfont{R}}} \newcommand{\Center}{\mathscr{Z}} \newcommand{\ad}{\operatorname{\ch@irxoperatorfont{ad}}} \newcommand{\Ad}{\operatorname{\ch@irxoperatorfont{Ad}}} \newcommand{\Conj}{\operatorname{\ch@irxoperatorfont{Conj}}} \newcommand{\acts}{\mathbin{\triangleright}} \newcommand{\racts}{\mathbin{\triangleleft}} \newcommand{\Char}{\ch@irxoperatorfont{char}} \newcommand{\modulo}{\operatorname{\ch@irxoperatorfont{mod}}} \newcommand{\Clifford}{\operatorname{\ch@irxoperatorfont{Cl}}} \newcommand{\cClifford}{\operatorname{\mathbb{C}\ch@irxoperatorfont{l}}} \newcommand{\Der}{\operatorname{\ch@irxoperatorfont{Der}}} \WithSuffix\newcommand\Der*{\decorate[^*]{\textrm{-}\Der}{}} \newcommand{\InnDer}{\operatorname{\ch@irxoperatorfont{InnDer}}} \WithSuffix\newcommand\InnDer*{\decorate[^*]{\textrm{-}\InnDer}{}} \newcommand{\OutDer}{\operatorname{\ch@irxoperatorfont{OutDer}}} \WithSuffix\newcommand\OutDer*{\decorate[^*]{\textrm{-}\OutDer}{}} \newcommand{\InnAut}{\operatorname{\ch@irxoperatorfont{InnAut}}} \WithSuffix\newcommand\InnAut*{\decorate[^*]{\textrm{-}\InnAut}{}} \newcommand{\OutAut}{\operatorname{\ch@irxoperatorfont{OutAut}}} \WithSuffix\newcommand\OutAut*{\decorate[^*]{\textrm{-}\OutAut}{}} \newcommand{\formal}[1]{\ch@irxllbbracket #1\ch@irxrrbbracket} \newcommand{\laurent}[1]{(\!(#1)\!)} \newcommand{\sweedler}[1]{{\scriptscriptstyle(#1)}} \newcommand{\algebras}{\categoryname{alg}} \WithSuffix\newcommand\algebras*{\decorate[^*]{\textrm{-}\algebras}{}} \newcommand{\Algebras}{\categoryname{Alg}} \WithSuffix\newcommand\Algebras*{\decorate[^*]{\textrm{-}\Algebras}{}} \newcommand{\reps}{\categoryname{rep}} \WithSuffix\newcommand\reps*{\decorate[^*]{\textrm{-}\reps}{}} \newcommand{\Reps}{\categoryname{Rep}} \WithSuffix\newcommand\Reps*{\decorate[^*]{\textrm{-}\Reps}{}} \newcommand{\PoissonAlg}{\categoryname{PoissonAlg}} \WithSuffix\newcommand\PoissonAlg*{\decorate[^*]{\textrm{-}\PoissonAlg}{}} \newcommand{\modules}{\categoryname{mod}} \WithSuffix\newcommand\modules*{\decorate[^*]{\textrm{-}\modules}{}} \newcommand{\Leftmodules}[1]{{#1}\textsf{-}\categoryname{mod}} \newcommand{\Rightmodules}[2][]{\categoryname{mod}_{#1}\textsf{-}{#2}} \newcommand{\Modules}{\categoryname{Mod}} \WithSuffix\newcommand\Modules*{\decorate[^*]{\textrm{-}\Modules}{}} \newcommand{\LeftModules}[1]{{#1}\textsf{-}\categoryname{Mod}} \newcommand{\RightModules}[2][]{\categoryname{Mod}_{#1}\textsf{-}{#2}} \newcommand{\Bimodules}{\categoryname{Bimod}} \WithSuffix\newcommand\Bimodules*{\decorate[^*]{\textrm{-}\Bimodules}{}} \newcommand{\Rings}{\categoryname{Ring}} \newcommand{\Groups}{\categoryname{Group}} \newcommand{\Ab}{\categoryname{Ab}} \newcommand{\Lattices}{\categoryname{Lattice}} \newcommand{\Sets}{\categoryname{Set}} \newcommand{\Vect}{\categoryname{Vect}} \newcommand{\LieAlgs}{\categoryname{LieAlg}} \newcommand{\Posets}{\categoryname{Poset}} \newcommand{\Directed}{\categoryname{Directed}} \newcommand{\GSets}[1][{G}]{{#1}\textrm{-}\Sets} \newcommand{\Groupoids}{\categoryname{Groupoid}} \fi \if@loadmath \newcommand{\vol}{\ch@irxoperatorfont{vol}} \newcommand{\complete}[1]{\widehat{#1}} \newcommand{\Ball}{\ch@irxoperatorfont{B}} \DeclarePairedDelimiter{\abs}{\lvert}{\rvert} \DeclarePairedDelimiter{\norm}{\lVert}{\rVert} \newcommand{\@supnormstar}[1]{\norm*{#1}_\infty} \newcommand{\@supnormnostar}[2][]{\norm[#1]{#2}_\infty} \newcommand{\supnorm}{\@ifstar\@supnormstar\@supnormnostar} \newcommand{\expands}[1][2.5]{\mathrel{\scalebox{#1}[1.1]{$\sim$}}} \newcommand{\std}{{\scriptscriptstyle{\ch@irxscriptfont{std}}}} \newcommand{\Weyl}{{\scriptscriptstyle{\ch@irxscriptfont{Weyl}}}} \newcommand{\Op}{\operatorname{Op}} \newcommand{\Opstd}{\operatorname{Op}_\std} \newcommand{\OpWeyl}{\operatorname{Op}_\Weyl} \newcommand{\spacename}[1]{\ch@irxspacefont{#1}} \newcommand{\Bounded}{\ch@irxspacefont{B}} \newcommand{\Continuous}{\ch@irxspacefont{C}} \newcommand{\Contbound}{\Continuous_{\mathrm{b}}} \newcommand{\Fun}[1][k]{\ch@irxspacefont{C}^{#1}} \newcommand{\Cinfty}{\Fun[\infty]} \newcommand{\Comega}{\Fun[\omega]} \newcommand{\Holomorphic}{\ch@irxspacefont{O}} \newcommand{\AntiHolomorphic}{\cc{\Holomorphic}} \newcommand{\Schwartz}{\ch@irxspacefont{S}} \newcommand{\Riemann}{\ch@irxspacefont{R}} \newcommand{\singsupp}{\operatorname{sing\,supp}} \newcommand{\seminorm}[1]{\mathrm{#1}} \newcommand{\ord}{\operatorname{ord}} \newcommand{\conv}{\operatorname{conv}} \newcommand{\extreme}{\operatorname{extreme}} \newcommand{\hilbert}[1]{\ch@irxhilbertfont{#1}} \newcommand{\prehilb}[1]{\ch@irxprehilbfont{#1}} \newcommand{\Adjointable}[1][{}]{\mathfrak{B}_{\scriptscriptstyle{#1}}} \newcommand{\Finite}[1][{}]{\mathfrak{F}_{\scriptscriptstyle{#1}}} \newcommand{\Compact}[1][{}]{\mathfrak{K}_{\scriptscriptstyle{#1}}} \newcommand{\opdomain}{\ch@irxhilbertfont{D}} \newcommand{\spec}{\operatorname{\ch@irxoperatorfont{spec}}} \newcommand{\closure}[1]{\overline{#1}} \newcommand{\res}{\operatorname{\ch@irxoperatorfont{res}}} \newcommand{\Res}{\operatorname{\ch@irxoperatorfont{Res}}} \newcommand{\specrad}{\operatorname{\varrho}} \newcommand{\slim}{\operatorname*{\ch@irxoperatorfont{s-lim}}} \newcommand{\wlim}{\operatorname*{\ch@irxoperatorfont{w-lim}}} \DeclarePairedDelimiter{\ketbr@}{\vert}{\vert} \DeclarePairedDelimiter{\ket}{\vert}{\rangle} \DeclarePairedDelimiter{\bra}{\langle}{\vert} \newcommand{\braket}[3][]{\SP[#1]{#2 \,#1\vert\, #3}} \newcommand{\ketbra}[3][]{\ketbr@[#1]{#2 #1\rangle #1\langle #3}} \newcommand{\Spec}{\operatorname{\ch@irxoperatorfont{Spec}}} \newcommand{\Rad}{\operatorname{\ch@irxoperatorfont{Rad}}} \newcommand{\ind}{\operatorname{\ch@irxoperatorfont{ind}}} \newcommand{\Measurable}{\ch@irxspacefont{M}} \newcommand{\Meas}{\ch@irxoperatorfont{Meas}} \newcommand{\BoundMeas}{\ch@irxspacefont{BM}} \newcommand{\Lp}[1][{p}]{\mathrm{L}^{#1}} \newcommand{\Lone}{\Lp[1]} \newcommand{\Ltwo}{\Lp[2]} \newcommand{\Linfty}{\Lp[\infty]} \newcommand{\Intp}[1][{p}]{\ch@irxspacefont{L}^{#1}} \newcommand{\Intone}{\Intp[1]} \newcommand{\Inttwo}{\Intp[2]} \newcommand{\Intinfty}{\Intp[\infty]} \newcommand{\essrange}{\operatorname{\ch@irxoperatorfont{ess\,range}}} \newcommand*{\esssup}{\operatorname*{\ch@irxoperatorfont{ess}\,\ch@irxoperatorfont{\sup}}} \newcommand{\@esssupnormstar}[1]{\norm*{#1}_{\esssup}} \newcommand{\@esssupnormnostar}[2][]{\norm[#1]{#2}_{\esssup}} \newcommand{\esssupnorm}{\@ifstar\@esssupnormstar\@esssupnormnostar} \newcommand{\ac}{\ch@irxscriptfont{ac}} \newcommand{\sing}{\ch@irxscriptfont{sing}} \newcommand{\indlim}{\operatorname*{{ind\,lim}}} \renewcommand{\projlim}{\operatorname*{{proj\,lim}}} \fi \if@loadmath \newcommand{\category}[1]{\ch@irxcategoryfont{#1}} \newcommand{\categoryname}[1]{\ch@irxcategorynamefont{#1}} \newcommand{\functor}[1]{\ch@irxfunctorfont{#1}} \newcommand{\groupoid}[1]{\ch@irxgroupoidfont{#1}} \newcommand{\source}{\ch@irxoperatorfont{source}} \newcommand{\target}{\ch@irxoperatorfont{target}} \newcommand{\unit}{\ch@irxoperatorfont{unit}} \newcommand{\opp}{\ch@irxscriptfont{opp}} \newcommand{\asso}{\ch@irxoperatorfont{asso}} \newcommand{\Hom}{\operatorname{\ch@irxoperatorfont{Hom}}} \newcommand{\End}{\operatorname{\ch@irxoperatorfont{End}}} \newcommand{\Aut}{\operatorname{\ch@irxoperatorfont{Aut}}} \WithSuffix\newcommand\Aut*{\decorate[^*]{\textrm{-}\Aut}{}} \newcommand{\Iso}{\operatorname{\ch@irxoperatorfont{Iso}}} \WithSuffix\newcommand\Iso*{\decorate[^*]{\textrm{-}\Iso}{}} \newcommand{\Obj}{\operatorname{\ch@irxoperatorfont{Obj}}} \newcommand{\Morph}{\operatorname{\ch@irxoperatorfont{Morph}}} \newcommand{\colim}{\operatorname*{{colim}}} \fi \if@loadmath \newcommand{\Lie}{\mathscr{L}} \DeclarePairedDelimiter{\ch@irxbracket}{[}{]} \DeclareMathDelimiter\ch@irxllbbracket{\mathopen}{stmry}{"4A}{stmry}{"71} \DeclareMathDelimiter\ch@irxrrbbracket{\mathclose}{stmry}{"4B}{stmry}{"79} \DeclarePairedDelimiter{\ch@irxbbracket}{\ch@irxllbbracket}{\ch@irxrrbbracket} \newcommand{\@schoutenstar}[1]{\ch@irxbbracket*{#1}_{\scriptscriptstyle\ch@irxscriptfont{S}}} \newcommand{\@schoutennostar}[2][]{\ch@irxbbracket[#1]{#2}_{\scriptscriptstyle\ch@irxscriptfont{S}}} \newcommand{\Schouten}{\@ifstar\@schoutenstar\@schoutennostar} \newcommand{\Forms}{\Omega} \newcommand{\ZdR}{\ch@irxoperatorfont{Z}_{\scriptscriptstyle\mathrm{dR}}} \newcommand{\BdR}{\ch@irxoperatorfont{B}_{\scriptscriptstyle\ch@irxscriptfont{dR}}} \newcommand{\HdR}{\ch@irxoperatorfont{H}_{\scriptscriptstyle\ch@irxscriptfont{dR}}} \newcommand{\Diffeo}{\operatorname{\ch@irxoperatorfont{Diffeo}}} \newcommand{\Diffop}{\operatorname{\ch@irxoperatorfont{DiffOp}}} \newcommand{\loc}{\ch@irxscriptfont{loc}} \newcommand{\germ}{\operatorname{\ch@irxoperatorfont{germ}}} \newcommand{\prol}{\ch@irxoperatorfont{prol}} \newcommand{\@nrbracketstar}[1]{\ch@irxbracket*{#1}_{\scriptscriptstyle\ch@irxscriptfont{NR}}} \newcommand{\@nrbracketnostar}[2][]{\ch@irxbracket[#1]{#2}_{\scriptscriptstyle\ch@irxscriptfont{NR}}} \newcommand{\NRbracket}{\@ifstar\@nrbracketstar\@nrbracketnostar} \newcommand{\@fnbracketstar}[1]{\ch@irxbracket*{#1}_{\scriptscriptstyle\ch@irxscriptfont{FN}}} \newcommand{\@fnbracketnostar}[2][]{\ch@irxbracket[#1]{#2}_{\scriptscriptstyle\ch@irxscriptfont{FN}}} \newcommand{\FNbracket}{\@ifstar\@fnbracketstar\@fnbracketnostar} \newcommand{\Manifolds}{\categoryname{\categoryname{Manifold}}} \newcommand{\lefttriv}{\ch@irxoperatorfont{left}} \newcommand{\righttriv}{\ch@irxoperatorfont{right}} \newcommand{\Gau}{\operatorname{\ch@irxoperatorfont{Gau}}} \newcommand{\Conn}{\operatorname{\ch@irxoperatorfont{Conn}}} \newcommand{\ratio}{\ch@irxoperatorfont{r}} \newcommand{\Parallel}{\operatorname{\ch@irxoperatorfont{P}}} \newcommand{\CE}{{\scriptscriptstyle{\ch@irxscriptfont{CE}}}} \newcommand{\HCE}{\ch@irxoperatorfont{H}_\CE} \newcommand{\fund}{\ch@irxoperatorfont{fund}} \newcommand{\Universal}{\operatorname{\ch@irxoperatorfont{U}}} \newcommand{\BCH}{\ch@irxscriptfont{\scriptscriptstyle{BCH}}} \newcommand{\LieGroups}{\categoryname{\categoryname{LieGroup}}} \newcommand{\Principal}{\categoryname{\categoryname{Principal}}} \newcommand{\GPrincipal}[1][G]{#1\categoryname{\textrm{-}\categoryname{Principal}}} \newcommand{\Fiber}{\categoryname{Fiber}} \newcommand{\FFiber}[1][F]{#1\categoryname{\textrm{-}\categoryname{Fiber}}} \newcommand{\Pin}{\group{Pin}} \newcommand{\Spin}{\group{Spin}} \newcommand{\nablaLC}{\nabla^{\scriptscriptstyle\ch@irxscriptfont{LC}}} \newcommand{\Laplace}{\Delta} \DeclareMathSymbol\dAlembert{\mathord}{AMSa}{"03} \newcommand{\feynman}[1]{\ooalign{$#1$\cr\hidewidth$\raise0.19ex\hbox{/}$\hidewidth\cr}} \newcommand{\Dirac}{\feynman{D}} \newcommand{\rotation}{\operatorname{\ch@irxoperatorfont{rot}}} \newcommand{\curl}{\operatorname{\ch@irxoperatorfont{curl}}} \newcommand{\divergence}{\operatorname{\ch@irxoperatorfont{div}}} \newcommand{\gradient}{\operatorname{\ch@irxoperatorfont{grad}}} \newcommand{\Tor}{\operatorname{\ch@irxoperatorfont{Tor}}} \newcommand{\Ric}{\operatorname{\ch@irxoperatorfont{Ric}}} \newcommand{\scal}{\operatorname{\ch@irxoperatorfont{scal}}} \newcommand{\Riem}{\operatorname{\ch@irxoperatorfont{Riem}}} \newcommand{\Hessian}{\ch@irxoperatorfont{Hessian}} \newcommand{\hodge}{\operatorname{\star}} \newcommand{\Nijenhuis}{\operatorname{\ch@irxoperatorfont{Nij}}} \newcommand{\del}{\mathop{}\!\partial} \newcommand{\delbar}{\mathop{}\!\cc{\partial}} \newcommand{\FS}{{\scriptscriptstyle{\ch@irxscriptfont{FS}}}} \newcommand{\Lift}{{\scriptscriptstyle{\ch@irxscriptfont{Lift}}}} \newcommand{\ver}{\ch@irxscriptfont{ver}} \newcommand{\hor}{\ch@irxscriptfont{hor}} \newcommand{\Ver}{\operatorname{\ch@irxoperatorfont{Ver}}} \newcommand{\Hor}{\operatorname{\ch@irxoperatorfont{Hor}}} \newcommand{\Sec}[1][k]{\Gamma^{#1}} \newcommand{\Secinfty}{\Sec[\infty]} \newcommand{\HolSec}{\Sec[]_{\ch@irxscriptfont{hol}}} \newcommand{\SymD}{\mathop{}\!\ch@irxoperatorfont{D}} \newcommand{\Densities}[1][n]{\abs{\Lambda^{#1}}} \newcommand{\MeasurableSections}{\ch@irxspacefont{M}\Sec[]} \newcommand{\IntpSections}[1][p]{\Intp[#1]\Sec[]} \newcommand{\IntegrableSections}{\IntpSections[1]} \newcommand{\Translation}{\ch@irxoperatorfont{T}} \newcommand{\frames}[1]{\ch@irxoperatorfont{#1}} \newcommand{\Frames}{\operatorname{\ch@irxoperatorfont{Frames}}} \newcommand{\FDiff}{\ch@irxoperatorfont{F}} \newcommand{\Sympl}{\operatorname{\ch@irxgroupfont{Sympl}}} \newcommand{\Jacobiator}[1][\pi]{\operatorname{\ch@irxoperatorfont{Jac}}_{#1}} \newcommand{\red}{\ch@irxscriptfont{red}} \newcommand{\Hess}{\ch@irxoperatorfont{Hess}} \newcommand{\KKS}{{\scriptscriptstyle\ch@irxscriptfont{KKS}}} \newcommand{\@courantstar}[1]{\ch@irxbbracket*{#1}_{\scriptscriptstyle\ch@irxscriptfont{C}}} \newcommand{\@courantnostar}[2][]{\ch@irxbbracket[#1]{#2}_{\scriptscriptstyle\ch@irxscriptfont{C}}} \newcommand{\Courant}{\@ifstar\@courantstar\@courantnostar} \newcommand{\@dorfmanstar}[1]{\ch@irxbbracket*{#1}_{\scriptscriptstyle\ch@irxscriptfont{D}}} \newcommand{\@dorfmannostar}[2][]{\ch@irxbbracket[#1]{#2}_{\scriptscriptstyle\ch@irxscriptfont{D}}} \newcommand{\Dorfman}{\@ifstar\@dorfmanstar\@dorfmannostar} \newcommand{\Dir}{\operatorname{\ch@irxoperatorfont{Dir}}} \newcommand{\Forward}{\mathcal{F}} \newcommand{\Backward}{\mathcal{B}} \newcommand{\Tangent}{\mathbb{T}} \newcommand{\MWreduction}{\big/\!\!\big/} \newcommand{\Mon}{\ch@irxoperatorfont{Mon}} \newcommand{\Hol}{\ch@irxoperatorfont{Hol}} \fi \if@loadmath \newcommand{\tr}{\operatorname{\ch@irxoperatorfont{tr}}} \newcommand{\rank}{\operatorname{\ch@irxoperatorfont{rank}}} \newcommand{\codim}{\operatorname{\ch@irxoperatorfont{codim}}} \newcommand{\diag}{\operatorname{\ch@irxoperatorfont{diag}}} \newcommand{\Trans}{{\ch@irxscriptfont{\scriptscriptstyle{T}}}} \newcommand{\Mat}{\ch@irxoperatorfont{M}} \newcommand{\SymMat}{\ch@irxoperatorfont{SymMat}} \newcommand{\ann}{\ch@irxscriptfont{ann}} \newcommand{\Span}[1][]{\operatorname{\ch@irxoperatorfont{span}_{#1}}} \newcommand{\basis}[1]{\ch@irxbasisfont{#1}} \renewcommand{\tensor}[1][{}]{\mathbin{\otimes_{\scriptscriptstyle{#1}}}} \newcommand{\Tensor}{\ch@irxoperatorfont{T}} \newcommand{\Anti}{\Lambda} \newcommand{\Sym}{\ch@irxoperatorfont{S}} \newcommand{\Symmetrizer}{\operatorname{\ch@irxoperatorfont{Sym}}} \newcommand{\AntiSymmetrizer}{\operatorname{\ch@irxoperatorfont{Alt}}} \newcommand{\ins}{\operatorname{\ch@irxoperatorfont{i}}} \newcommand{\jns}{\operatorname{\ch@irxoperatorfont{j}}} \newcommand{\insa}{\ins_{\ch@irxscriptfont{a}}} \newcommand{\inss}{\ins_{\ch@irxscriptfont{s}}} \newcommand{\degs}{\ch@irxoperatorfont{deg}_{\ch@irxscriptfont{s}}} \newcommand{\dega}{\ch@irxoperatorfont{deg}_{\ch@irxscriptfont{a}}} \DeclarePairedDelimiter{\SP} {\langle}{\rangle} \newcommand{\littlepara}{{\scriptscriptstyle\parallel}} \newcommand{\IP}[6][{}]{\decorate*[^{#2}_{#3}]{\SP[#1]{#4}}{^{#5}_{#6}}} \fi \if@loadmath \newcommand{\EX}{\operatorname{\ch@irxoperatorfont{E}}} \newcommand{\Var}{\operatorname{\ch@irxoperatorfont{Var}}} \newcommand{\Cov}{\operatorname{\ch@irxoperatorfont{Cov}}} \newcommand{\Cor}{\operatorname{\ch@irxoperatorfont{Cor}}} \fi \if@loadmath \newcommand{\cl}{\ch@irxscriptfont{cl}} \newcommand{\scl}{\ch@irxscriptfont{scl}} \newcommand{\interior}{\circ} \newcommand{\boundary}{\partial} \newcommand{\supp}{\operatorname{\ch@irxoperatorfont{supp}}} \newcommand{\dist}{\operatorname{\ch@irxoperatorfont{dist}}} \newcommand{\topology}[1]{\ch@irxtopologyfont{#1}} \newcommand{\filter}[1]{\ch@irxfilterfont{#1}} \newcommand{\sheaf}[1]{\ch@irxsheaffont{#1}} \newcommand{\Sections}{\operatorname{\ch@irxoperatorfont{Sections}}} \newcommand{\HOM}{\operatorname{\ch@irxsheaffont{H}\!\mathit{om}}} \DeclarePairedDelimiter{\etale}{\lvert}{\rvert} \newcommand{\topological}{\categoryname{top}} \newcommand{\Topological}{\categoryname{Top}} \newcommand{\Sheaves}{\categoryname{Sheaves}} \newcommand{\PreSheaves}{\categoryname{PreSheaves}} \newcommand{\Etale}{\categoryname{Etale}} \fi \endinput %% %% End of file `nchairx.sty'.