\newsavebox{\kD}
\savebox{\kD}(7,7){
\begin{picture}(7,7)
 \put(7,0){\line(-1,0){7}}
\put(7,0){\line(0,1){7}}
%\put(1,6){\makebox(0,0){$\cdot$}}
\end{picture}}
\newcommand{\kart}{\ar @{} [dr] |{\begin{picture}(7,7)
 \put(0,0){\usebox{\kD}}
\end{picture}}}

\newsavebox{\ukD}
\savebox{\ukD}(7,7){
\begin{picture}(7,7)
 \put(0,0){\line(1,0){7}}
\put(0,0){\line(0,1){7}}
%\put(1,6){\makebox(0,0){$\cdot$}}
\end{picture}}
\newcommand{\ukart}{\ar @{} [dr] |{\begin{picture}(7,7)
 \put(0,0){\usebox{\ukD}}
\end{picture}}}
\newcommand{\swkart}{\ar @{} [dr] |{\begin{picture}(7,7)
 \put(0,0){\usebox{\ukD}}
\end{picture}}}

\newsavebox{\nekD}
\savebox{\nekD}(7,7){
\begin{picture}(7,7)
 \put(0,7){\line(-1,0){7}}
\put(0,7){\line(0,-1){7}}
%\put(1,6){\makebox(0,0){$\cdot$}}
\end{picture}}
\newcommand{\nekart}{\ar @{} [dr] |{\begin{picture}(7,7)
 \put(0,0){\usebox{\nekD}}
\end{picture}}}

\newsavebox{\ckD}
\savebox{\ckD}(7,7){
\begin{picture}(7,7)
 \put(0,7){\line(0,-1){7}}
\put(0,7){\line(1,0){7}}
%\put(6,1){\makebox(0,0){$\cdot$}}
\end{picture}}
\newcommand{\kokart}{\ar @{} [dr] |{\begin{picture}(7,7)
 \put(0,0){\usebox{\ckD}}
\end{picture}}}

 \newcommand*{\main}[1]{\textbf{\hyperpage{#1}}}
 %\newcommand{\eref}[2]{\cite{#2} \ref{#1}}
 %\newcommand{\rref}[2]{\cite{#2} \ref{#1}}
\newcommand{\eref}[2]{\cite{#2} \ref{#2-#1}}
 \newcommand{\rref}[2]{\cite{#2} \ref{#2-#1}}


\newcommand{\squap}{\mathbin{\sqcup\hspace{-8pt}\sqcap}}
\renewcommand{\amalg}{\sqcup}
\renewcommand{\coprod}{\bigsqcup}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Abk"urzungen f"ur Pfeile
%\newcommand{\dau}{{\downarrow\!\upharpoonleft}}
\newcommand{\dau}{{\downarrow\!\cup}}
\newcommand{\ra}{\rightarrow}
\newcommand{\lea}{\leftarrow}
\newcommand{\lra}{\longrightarrow}
\newcommand{\sra}{\twoheadrightarrow}
\newcommand{\hra}{\hookrightarrow}
\newcommand{\hsira}{\mathrel{\stackrel{\sim}{\hookrightarrow}}}
\newcommand{\hla}{\hookleftarrow}
%\newcommand{\sira}{\stackrel{\sim}{\rightarrow}}
\newcommand{\sira}{\mathrel{\mathbin{\overset{\scriptscriptstyle \sim}{\rule{0pt}{4pt}\smash{\ra}}}}}
\newcommand{\sila}{\mathrel{\mathbin{\overset{\scriptscriptstyle \sim}{\rule{0pt}{4pt}\smash{\leftarrow}}}}}
%\newcommand{\sirra}{\stackrel{\approx}{\rightarrow}}
\newcommand{\sirra}{\mathrel{\overset{\scriptscriptstyle \approx}{\rule{0pt}{4pt}\smash{\rightarrow}}}}
\newcommand{\silla}{\mathrel{\overset{\scriptscriptstyle \approx}{\rule{0pt}{4pt}\smash{\leftarrow}}}}
\newcommand{\sirla}{\mathrel{\overset{\scriptscriptstyle \approx}{\rule{0pt}{4pt}\smash{\leftrightarrow}}}}
\newcommand{\siRa}{\mathrel{\mathbin{\overset{\scriptscriptstyle \sim}{\rule{0pt}{4pt}\smash{\Rightarrow}}}}}
%\newcommand{\siRa}{\mathrel{\stackrel{\sim}{\Rightarrow}}}
\newcommand{\leftiso}{\mathrel{\stackrel{\sim}{\leftarrow}}}
\newcommand{\da}{\downarrow}
\newcommand{\ua}{\uparrow}
\newcommand{\RA}{\Rightarrow}
\newcommand{\IFF}{\Leftrightarrow}
\newcommand{\leftmapsto}{\mapsfrom}
 % \newcommand{\downmapsto} ist definiert in MitKapitelVorspann.tex
 % und OhneKapitelVorspann.tex, funktioniert aber nur bei pdflatex
 % mit der Option final. Bei normalem Latex und ohne Option final
 % als Synonym von \downarrow eingestellt.

\newcommand{\hri}{\mathrel{\stackrel{\scriptscriptstyle{\shortmid\sim\shortmid}}{\ra}}}
\newcommand{\hli}{\mathrel{\stackrel{\scriptscriptstyle{\shortmid\sim\shortmid}}{\leftarrow}}}
\newcommand{\vra}{\mathrel{\overset{\scriptscriptstyle \sim}{\rule{0pt}{4pt}\smash{\hra}}}}
\newcommand{\vla}{\mathrel{\overset{\scriptscriptstyle \sim}{\rule{0pt}{4pt}\smash{\hla}}}}
\newcommand{\aeq}{\mathrel{\overset{\scriptscriptstyle -}{\rule{0pt}{4pt}\smash{\ra}}}}
\newcommand{\saeq}{\mathrel{\overset{\scriptscriptstyle -}{\rule{0pt}{4pt}\smash{\sra}}}}
\newcommand{\haeq}{\mathrel{\overset{\scriptscriptstyle -}{\rule{0pt}{4pt}\smash{\hra}}}}
\newcommand{\Hri}{\mathrel{\stackrel{\scriptscriptstyle{\shortmid\sim\shortmid}}{\RA}}}
\newcommand{\qri}{\mathrel{\breve{\ra}}}%{\stackrel{\scriptscriptstyle{\shortpar
%\newcommand{\aeq}{\mathrel{\bar{\ra}}}% allel\sim\shortparallel}}{\ra}}
\newcommand{\qli}{\mathrel{\breve{\leftarrow}}}%{\stackrel{\scriptscriptstyle{\shortparallel\sim\shortparallel}}{\leftarrow}}
\newcommand{\sirad}{\hri}
\newcommand{\acts}{{\raisebox{.15em}{$\scriptstyle\ssearrow$}}}
  %Operation einer Gruppe auf einem Raum, textstyle
\newcommand{\sacts}{{\raisebox{.09em}{$\scriptscriptstyle\ssearrow$}}}
 %Operation einer Gruppe auf einem Raum, scriptstyle
\newcommand{\uvec}{\hspace{-4pt}{\vec{}}\hspace{4.5pt}}
 %Pfeile als oberer Index hinter Universen 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Abk"urzungen F"ur Griechische Buchstaben
\newcommand{\al}{\alpha}
\newcommand{\La}{\Lambda}
\newcommand{\va}{\varphi}
\newcommand{\ga}{{\gamma}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Blackboardboldface
\newcommand{\Bl}[1]{{\mathbb{#1}}}
\newcommand{\DK}{\Bl{K}}
\newcommand{\DC}{\Bl{C}}
\newcommand{\DD}{\Bl{D}}
\newcommand{\vDC}{{{\DC\hspace{-2mm}\cdot}\hspace{1mm}}}
\newcommand{\DP}{\Bl{P}}
\newcommand{\DR}{\Bl{R}}
\newcommand{\DZ}{\Bl{Z}}
\newcommand{\DN}{\Bl{N}}
\newcommand{\DQ}{\Bl{Q}}
\newcommand{\DV}{\Bl{V}}
\newcommand{\tT}{{\op{\underaccent{\bar}{T}}}}
\newcommand{\td}{{\op{\underaccent{\bar}{d}}}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Index
\newcommand{\defind}[1]{{\bf #1}\index{#1}}
\newcommand{\defnoind}[1]{{\bf #1}}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Spezialsymbole
%\newcommand{\wint}{\oint}


\newcommand{\UT}{I}%Einheit von Tensorkategorie
\newcommand{\awq}{!}%fuer $exists!$ im Index!
\newcommand{\op}{\operatorname}
\newcommand{\ph}{\op}%für physikalische Einheiten
\newcommand{\diff}{\operatorname{d}\!}
\newcommand{\tiff}{{\operatorname{T}}} 
\newcommand{\co}{\mathrel{{\subset}\!\;\!\!\!\!{\circ}}}
%\newcommand{\co}{\mathrel
% {\mbox{$\subset$\hspace{-1,1ex}\raisebox{0,15ex}{${\scriptstyle
% \circ\;}$}}}}
\newcommand{\dcurlyvee}{\mathbin{\dot\curlyvee}}
\newcommand{\dcurlywedge}{\mathbin{\mathrm{\underaccent{\dot}{\curlywedge}}}}
\newcommand{\hotimes}{\mathbin{\hat\otimes}}
\newcommand{\botimes}{\mathbin{\bar\otimes}}
\newcommand{\bwedge}{\mathbin{\bar\wedge}}
\newcommand{\vapprox}{\mathbin{\text{\rotatebox[origin=c]{90}{$\approx$}}}}
\newcommand{\kP}{\raisebox{0,4ex}{$\scriptscriptstyle\ra$}}
\newcommand{\skP}{\raisebox{0,18ex}{$\scriptscriptstyle\ra$}}
%\newcommand{\As}{\mathrel{\mbox{$\subset\hspace{-1,9ex}$ {${\scriptstyle \bigwedge}$}}}}
%\newcommand{\As}{\mathrel{\subset\mkern-15mu\mathchoice{\mkern-2mu}{}{}{}{\scriptstyle \bigwedge}}}
\newcommand{\lAs}{\mathchoice{\mathrel{\supset\mkern-19mu{\scriptstyle \bigwedge}}}
{\mathrel{\supset\mkern-19mu{\scriptstyle \bigwedge}}}
{\mathrel{\supset\mkern-14mu {\scriptscriptstyle \bigwedge}}}
{\mathrel{\supset\mkern-15mu {\scriptscriptstyle \wedge}}}}

\newcommand{\As}{\mathchoice{\mathrel{\subset\mkern-15mu{\scriptstyle \bigwedge}}}
{\mathrel{\subset\mkern-15mu{\scriptstyle \bigwedge}}}
{\mathrel{\subset\mkern-11mu {\scriptscriptstyle \bigwedge}}}
{\mathrel{\subset\mkern-12mu {\scriptscriptstyle \wedge}}}}

\newcommand{\lco}{\mathrel{{{\supset}\!\!\;\!\!\!\!{\circ}}}}
\newcommand{\vsqcup}{\mathrel{\vec\sqcup}}
\newcommand{\shriek}{\text{!`}}

\newcommand{\intHom}{{\operatorname{Hom}
\mkern-27.8mu\raisebox{0.22mm}{\text{\tiny $\times$}} \mkern14.4mu}}
\newcommand{\Thom}{{\leftarrow\!\!\!\!\!\!{\otimes}}}
\newcommand{\Adjtr}{{\otimes\!\!\succ}}
\newcommand{\Adjtl}{{\prec\!\!\otimes}}
\newcommand{\pdef}{\mathrel{\mathop:}=}
\newcommand{\defp}{\mathrel=\!{\mathop:}\;}%{\eqqcolon}
\newcommand{\llangle}{\langle\!\langle}
\newcommand{\rrangle}{\rangle\!\rangle}
\newcommand{\frei}{^{\scriptscriptstyle \nnwarrow}}

\newenvironment{Bild}{\begin{figure}[p]\centering}{\end{figure}}%\stepcounter{figs}\stepcounter{figc}}
\newenvironment{fBild}{\begin{figure}}{\end{figure}}%\stepcounter{figs}\stepcounter{figc}}
\newcommand{\vEns}{\op{E}\!\!\stackrel{\leftarrow}{\op{ns}}} 
\newcommand{\FAKK}{!}
\DeclareMathOperator{\Liel}{\textup{\rm L\`{\i}e}}
\DeclareMathOperator{\Lier}{\textup{\rm L\'{\i}e}}
\DeclareMathOperator{\Enso}{\textup{\rm E\r{n}s}}
\DeclareMathOperator*{\Toph}{\textup{\rm T\hspace{-1pt}\^{o}p}}
\DeclareMathOperator{\Homo}{\textup{\rm H\r{o}m}}
\DeclareMathOperator*{\limh}{\underrightarrow{\textup{\rm l\^{\i}m}}}
\DeclareMathOperator*{\colf}{colf}
\DeclareMathOperator*{\col}{col}
\DeclareMathOperator*{\limf}{limf}
\DeclareMathOperator*{\colim}{colim}
\DeclareMathOperator*{\varinjcol}{\underrightarrow{\textup{\rm col}}}
\DeclareMathOperator*{\colh}{\textup{\rm c\^{o}l}}
\DeclareMathOperator*{\colhu}{\textup{\rm c\^{o}lf}}
\DeclareMathOperator*{\limc}{\textup{\rm l\v{\i}m}}
\DeclareMathOperator*{\limcu}{\textup{\rm l\v{\i}mf}}
\DeclareMathSymbol{\shortminus}{\mathbin}{AMSa}{"39}

\newcommand{\ooplus}{\operatornamewithlimits{\oplus}}

\DeclareMathOperator*{\kv}{\textup{!`}} 


\newcommand{\wint}{\mathop{\mathpalette\docircint\relax}\!\int}
\newcommand{\docircint}[2]{%
  \ifx#1\displaystyle
    \displaycircint
  \else
    \normalcircint{#1}%
  \fi
}
\newcommand{\displaycircint}{\displaystyle\mathsf{c}\mkern-18mu}
\newcommand{\normalcircint}[1]{%
  \smallerc{#1}\ifx#1\textstyle\mkern-8.3mu\else\mkern-8.2mu\fi
}
\newcommand{\smallerc}[1]{%
  \vcenter{\hbox{$\ifx#1\textstyle\scriptstyle\else\scriptscriptstyle\fi\mathsf{c}$}}%
}

\newcommand{\Wint}{\wint}

\newcommand{\ttop}{{\scriptscriptstyle \top}}



%%% Local Variables: 
%%% mode: plain-tex
%%% TeX-master: "AATOTAL"
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