% This file: (find-LATEX "edrx21defs.tex")
%       See: (find-LATEX "edrx17defs.tex")
%            (find-LATEX "edrx15defs.tex")
% Loaded by: (find-LATEX "edrx21.sty")
% Version:   2023oct07  <- don't trust this date
%
% Miscellaneous defs, mostly symbols.


% «.categories»			(to "categories")
% «.greek-letters»		(to "greek-letters")
% «.combinators»		(to "combinators")
% «.colors»			(to "colors")
% «.mystrut»			(to "mystrut")
% «.bhbox»			(to "bhbox")
% «.bgcolorhbox»		(to "bgcolorhbox")
% «.firstcol-anothercol»	(to "firstcol-anothercol")
% «.co»				(to "co")
% «.ifundefined»		(to "ifundefined")
% «.cells»			(to "cells")


\def\N{\mathbb{N}}
\def\Q{\mathbb{Q}}
\def\R{\mathbb{R}}
\def\Z{\mathbb{Z}}


% «categories»  (to ".categories")
%
\def\Set {\mathbf{Set}}
\def\Sets{\mathbf{Sets}}
\def\Cat {\mathbf{Cat}}
\def\Grp {{\bf Grp}}
\def\Mon {{\bf Mon}}
\def\PTop{{\bf PTop}}
\def\Top {{\bf Top}}
\def\Vect{{\bf Vect}}
%
\def\catA{\mathbf{A}}
\def\catB{\mathbf{B}}
\def\catC{\mathbf{C}}
\def\catD{\mathbf{D}}
\def\catE{\mathbf{E}}
\def\catH{\mathbf{H}}
\def\catI{\mathbf{I}}
\def\catJ{\mathbf{J}}
\def\catP{\mathbf{P}}
%\def\OX{{\mathcal{O}_X}}
%\def\E{\mathbf{E}}
%\def\T{\mathbf{T}}
%\def\SetI{{\Set^{\mathbb{I}}}}
%\def\SetF{{\Set^{\mathcal{F}}}}
%\def\SetU{{\Set^{\mathcal{U}}}}
%\def\SetP{{\Set^{\mathbf{P}}}}
%\def\SetM{{\Set^{\mathbf{M}}}}
%\def\SetC{{\Set^{\bf C}}}
%\def\bbA{\mathbb{A}}
%\def\bbB{\mathbb{B}}
%\def\bbC{\mathbb{C}}
%\def\bbD{\mathbb{D}}
%\def\bbE{\mathbb{E}}
%\def\bbH{\mathbb{H}}
%\def\bbV{\mathbb{V}}





% Quantificadores,
%
\def\Ex{\exists}
\def\Fa{\forall}
%\def\Exob#1{\mathop{\exists\;{#1}}}
%\def\Exbangob#1{\mathop{\exists!\;{#1}}}
%\def\Faob#1{\mathop{\forall\;{#1}}}
%\def\Exbang{\exists!}

\def\void {\varnothing}
\def\bsl  {\backslash}
\def\False{\Finv}
\def\nat  {\natural}



% «greek-letters»  (to ".greek-letters")
%
\def\aa{\alpha}
\def\bb{\beta}
\def\cc{\gamma}
\def\dd{\delta}
%\def\ee{\epsilon}
\def\ee{\varepsilon}    % (find-texbookpage (+ 12 128) "\\varepsilon")
\def\gg{\gamma}
\def\kk{\kappa}
\def\ww{\omega}
\def\Om{\Omega}
\def\Th{\Theta}
\def\GG{\Gamma}
\def\DD{\Delta}
\def\LL{\Lambda}
%
% (find-es "tex" "varphi")
%\let\origphi=\phi
%\def\phi{\varphi}

\def\superscriptOne  {^1}
\def\superscriptTwo  {^2}
\def\superscriptThree{^3}



\def\calA{\mathcal{A}}
\def\calB{\mathcal{B}}
\def\calC{\mathcal{C}}
\def\calD{\mathcal{D}}
\def\calE{\mathcal{E}}
\def\calF{\mathcal{F}}
\def\calG{\mathcal{G}}
\def\calL{\mathcal{L}}
\def\calN{\mathcal{N}}
\def\calR{\mathcal{R}}
\def\calV{\mathcal{V}}



\def\id   {\mathrm{id}}
\def\ev   {\mathrm{ev}}
\def\cur  {\operatorname{\textsf{cur}}}
\def\uncur{\operatorname{\textsf{uncur}}}
\def\app  {\operatorname{app}}

\def\compr{\operatorname{compr}}
\def\Int  {\operatorname{Int}}

\def\adj   {\operatorname{adj}}

\def\hom   {\operatorname{hom}}
\def\Hom   {\operatorname{Hom}}
\def\op    {{\operatorname{op}}}
\def\colim {{\operatorname{colim}}}
\def\Colim {{\operatorname{Colim}}}
\def\Lim   {{\operatorname{Lim}}}
\def\src   {\operatorname{src}}
\def\tgt   {\operatorname{tgt}}
\def\dom   {\operatorname{dom}}
\def\cod   {\operatorname{cod}}
\def\Cod   {\operatorname{Cod}}
\def\Sub   {\operatorname{Sub}}
\def\CanSub{\operatorname{CanSub}}
\def\Objs  {\operatorname{Objs}}

\def\Props {\operatorname{Props}}
\def\Prfs  {\operatorname{Prfs}}
\def\prf   {\operatorname{prf}}

\def\fv     {\operatorname{fv}}
\def\FV     {\operatorname{FV}}
\def\welldef{{\operatorname{wd}}}
\def\welld  {{\operatorname{wd}}}




\def\setof    #1{\{\,#1\,\}}
\def\setofst#1#2{\{\,#1\;|\;#2\,\}}
\def\setofsc#1#2{\{\,#1\;;\;#2\,\}}
\def\Pts        {\mathcal{P}}



\def\ovl{\overline}

\def\nameof#1{\ulcorner#1\urcorner}
%
% (find-es "tex" "llangle-and-rrangle")
% (find-es "tex" "llbracket-and-rrbracket")
%
\def\llangle{\langle\!\langle}
\def\rrangle{\rangle\!\rangle}
\def\ang #1{\langle #1 \rangle}
\def\angg#1{\llangle#1\rrangle}
\def\angc  {\ang{\,,}}
%\def\<{\langle}
%\def\>{\rangle}
%
% Bananas
\def\ban#1{(\mskip-1.2\thinmuskip| #1 |\mskip-1.2\thinmuskip)}







% Calculus:
\def\sen   {\operatorname{sen}}
\def\arcsen{\operatorname{arcsen}}
\def\sec   {\operatorname{sec}}
\def\arcsec{\operatorname{arcsec}}

\def\uu{\vec u}
\def\vv{\vec v}
\def\ww{\vec w}
\def\Vec#1{{\overrightarrow{#1}}}
\def\VEC#1{{\overrightarrow{(#1)}}}



% «combinators»  (to ".combinators")
%
\def\cbS{\mathbf{S}}
\def\cbK{\mathbf{K}}
\def\cbI{\mathbf{I}}
\def\cbP{\mathbf{P}}
\def\cbD{\mathbf{D}}
\def\cbV{\mathbf{V}}
\def\cbT{\mathbf{T}}
\def\cbF{\mathbf{F}}
\def\SKI{\mathbf{SKI}}


% «colors»  (to ".colors")
% Mainly for slides.
%
\long\def\ColorRed   #1{{\color{Red1}#1}}
\long\def\ColorViolet#1{{\color{MagentaVioletLight}#1}}
\long\def\ColorViolet#1{{\color{Violet!50!black}#1}}
\long\def\ColorGreen #1{{\color{SpringDarkHard}#1}}
\long\def\ColorGreen #1{{\color{SpringGreenDark}#1}}
\long\def\ColorGreen #1{{\color{SpringGreen4}#1}}
\long\def\ColorGray  #1{{\color{GrayLight}#1}}
\long\def\ColorGray  #1{{\color{black!30!white}#1}}
\long\def\ColorBrown #1{{\color{Brown}#1}}
\long\def\ColorBrown #1{{\color{brown}#1}}
\long\def\ColorOrange#1{{\color{orange}#1}}
\long\def\ColorBlack #1{{\color{black}#1}}

% See: (find-es "tex" "xcolor")
%      (find-es "tex" "xcolor" "fcolorbox")
\def\standout#1{\fcolorbox{red}{yellow}{#1}}


% «mystrut»  (to ".mystrut")
% (find-es "tex" "mathstrut")
\def\mystrut#1#2{{\setbox0=\hbox{} \ht0=#1 \dp0=#2 \box0}}


% «bhbox»  (to ".bhbox")
% See: (find-es "tex" "bhbox")
\def\smashedvrule#1#2#3{\vrule width#1 height#2 depth#3 \kern-#1}
\def\bhboxuppercolor{yellow}
\def\bhboxlowercolor{orange}
\def\bhboxm#1{\bhbox{$#1$}}
\def\bhbox #1{\hbox{\bhboxz{#1}}}
\def\bhboxz#1{%
    \setbox0\hbox{#1}%
    {\color{\bhboxuppercolor}{\smashedvrule{\wd0}{\ht0}{0pt}}}%
    {\color{\bhboxlowercolor}{\smashedvrule{\wd0}{0pt}{\dp0}}}%
    \box0%
  }

% «bgcolorhbox»  (to ".bgcolorhbox")
% See: (find-dednat6 "tug-slides.tex" "bgcolorhbox")
\def\bgcolorhbox#1#2{{%
  \setbox0\hbox{#2}%
  \setbox0\vbox{\vskip\fboxsep\box0\vskip\fboxsep}%
  \setbox0\hbox{\kern\fboxsep\box0\kern\fboxsep}%
  {\color{#1}{\smashedvrule{\wd0}{\ht0}{\dp0}}}%
  \box0%
  }}


% «firstcol-anothercol»  (to ".firstcol-anothercol")
% (find-es "tex" "firstcol-anothercol")
\def\colwidth{8cm}
\long\def\firstcol#1{\begin{minipage}[t]{\colwidth} #1 \end{minipage}}
\long\def\anothercol#1{\qquad\firstcol{#1}}

% «co»  (to ".co")
% (find-es "tex" "co")
% (find-es "tex" "poor-mans-code")
% \co: a low-level way to typeset code; a poor man's "\verb"
% It conflicts with the `\co' of Category Theory =(
\def\co#1{{%
  \def\%{\char37}%
  \def\\{\char92}%
  \def\^{\char94}%
  \def\~{\char126}%
  \tt#1%
  }}
\def\qco#1{`\co{#1}'}
\def\qqco#1{``\co{#1}''}


% «ifundefined»  (to ".ifundefined")
% (find-es "tex" "ifundefined")
\def\ifundefined#1{\expandafter\ifx\csname#1\endcsname\relax}


% «cells»  (to ".cells")
% (find-es "tex" "picture-cells")
% (find-es "tex" "ifx")
% (find-dn6 "preamble6.lua" "preamble1" "\\def\\cell")
\ifundefined  {celllower} \newlength {\celllower} \fi
\ifundefined {lcelllower} \newlength{\lcelllower} \fi
 \celllower=3pt    % For \documentclass[10pt]{...}
%\celllower=3.5pt  % For \documentclass[12pt]{...}

\def\cellfont{}
\def\lcellfont{}
\def\cell #1{\lower\celllower\hbox to 0pt{\hss\cellfont${#1}$\hss}}
\def\lcell#1{\lower\celllower\hbox to 0pt   {\lcellfont${#1}$\hss}}

% (find-es "tex" "ifx")
% (find-LATEX "material-para-GA.tex" "cells" "\\def\\cellnw")
\def\cellhr#1{\hbox to 0pt    {\cellfont${#1}$\hss}}
\def\cellhc#1{\hbox to 0pt{\hss\cellfont${#1}$\hss}}
\def\cellhl#1{\hbox to 0pt{\hss\cellfont${#1}$}}
\def\cellva#1{\setbox0#1\raise \dp0       \box0}
\def\cellvm#1{\setbox0#1\lower \celllower \box0}
\def\cellvb#1{\setbox0#1\lower \ht0       \box0}

\def\cellnw  #1{\cellva{\cellhl{#1}}}
 \def\celln  #1{\cellva{\cellhc{#1}}}
  \def\cellne#1{\cellva{\cellhr{#1}}}
\def\cellw   #1{\cellvm{\cellhl{#1}}}
 \def\celle  #1{\cellvm{\cellhr{#1}}}
\def\cellsw  #1{\cellvb{\cellhl{#1}}}
 \def\cells  #1{\cellvb{\cellhc{#1}}}
  \def\cellse#1{\cellvb{\cellhr{#1}}}

\ifundefined {cellsep} \newdimen\cellsep \fi
\cellsep=4pt
\def\addcellsep{%
  \setbox0=\hbox{\kern\cellsep\box0\kern\cellsep}%
  \ht0=\ht0 plus \cellsep%
  \dp0=\dp0 plus \cellsep%
  \box0%
}
\def\cellsp#1{%
  \setbox0=\hbox{#1}%
  \addcellsep%
  \box0%
}





\def\frown{\ensuremath{{=}{(}}}
\def\smile{\ensuremath{{=}{)}}}
\def\True {\mathbf{V}}
\def\False{\mathbf{F}}
\def\D    {\displaystyle}
\def\ph   {\phantom}


%\def\comp {\operatorname{comp}}

%\def\und#1{{\underline{#1}}}
% Often redefined to:
%\def\und#1#2{\underbrace{#1}_{#2}}














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