% (find-LATEX "2020genericfigures.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2020genericfigures.tex" :end))
% (defun d () (interactive) (find-pdf-page      "~/LATEX/2020genericfigures.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2020genericfigures.pdf"))
% (defun e () (interactive) (find-LATEX "2020genericfigures.tex"))
% (defun u () (interactive) (find-latex-upload-links "2020genericfigures"))
% (defun v () (interactive) (find-2a '(e) '(d)) (g))
%      (code-eec-LATEX "2020genericfigures")
% (find-lualatex-links "2020genericfigures")
% (find-pdf-page   "~/LATEX/2020genericfigures.pdf")
% (find-sh0 "cp -v  ~/LATEX/2020genericfigures.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2020genericfigures.pdf /tmp/pen/")
%   file:///home/edrx/LATEX/2020genericfigures.pdf
%               file:///tmp/2020genericfigures.pdf
%           file:///tmp/pen/2020genericfigures.pdf
% http://angg.twu.net/LATEX/2020genericfigures.pdf
% (find-LATEX "2019.mk")

% «.1._the-cat-of-C-sets»	(to "1._the-cat-of-C-sets")
% «.1.1._examples-of-C-sets»	(to "1.1._examples-of-C-sets")
% «.2.2._yoneda-lemma»		(to "2.2._yoneda-lemma")
% «.djvuize»			(to "djvuize")

\documentclass[oneside,12pt]{article}
\usepackage[colorlinks,citecolor=DarkRed,urlcolor=DarkRed]{hyperref} % (find-es "tex" "hyperref")
%\usepackage[hyphenbreaks]{breakurl}     % (find-es "tex" "breakurl")
%\usepackage[anythingbreaks]{breakurl}   % (find-es "tex" "breakurl")
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{pict2e}
\usepackage[x11names,svgnames]{xcolor} % (find-es "tex" "xcolor")
%\usepackage{colorweb}                 % (find-es "tex" "colorweb")
%\usepackage{tikz}
%
% (find-dn6 "preamble6.lua" "preamble0")
\usepackage{proof}   % For derivation trees ("%:" lines)
\input diagxy        % For 2D diagrams ("%D" lines)
\xyoption{curve}     % For the ".curve=" feature in 2D diagrams
%
\usepackage{edrx15}               % (find-LATEX "edrx15.sty")
\input edrxaccents.tex            % (find-LATEX "edrxaccents.tex")
\input edrxchars.tex              % (find-LATEX "edrxchars.tex")
\input edrxheadfoot.tex           % (find-LATEX "edrxheadfoot.tex")
\input edrxgac2.tex               % (find-LATEX "edrxgac2.tex")
%
% (find-es "tex" "geometry")
\begin{document}

\catcode`\^^J=10
\directlua{dofile "dednat6load.lua"}  % (find-LATEX "dednat6load.lua")

\def\C{\mathbb{C}}

% (find-books "__cats/__cats.el" "reyes")
% (find-reyeszolfpage  11 "1 The category of C-Sets")
% (find-reyeszolftext  11 "1 The category of C-Sets")
% (find-reyeszolfpage  12   "a C-Set is a functor")
% (find-reyeszolftext  12   "a C-Set is a functor")
% (find-reyeszolfpage  12 "1.1 Examples of C-Sets")
% (find-reyeszolfpage  19 "1.2 Monomorphism, epimorphism, isomorphism")
% (find-reyeszolfpage  22 "2 Representable C-sets and Yoneda lemma")
% (find-reyeszolfpage  23 "2.1 Computation of representable -sets in the examples")
% (find-reyeszolfpage  29 "2.2 Yoneda lemma")
% (find-reyeszolfpage  30 "3 A C-set as a container of generic figures")
% (find-reyeszolfpage  32 "3.1 Glueing in the examples")
% (find-reyeszolfpage  34 "3.2 Glueing schemes as categories")




{\setlength{\parindent}{0em}
\footnotesize

Notes on Reyes/Reyes/Zolfaghari's book

``Generic figures and their glueings: A constructive approach to functor categories''

(Polimetrica, 2004).

\url{https://reyes-reyes.com/2004/06/01/generic-figures-and-their-glueings-a-constructive-approach-to-functor-categories/}

\url{https://marieetgonzalo.files.wordpress.com/2004/06/generic-figures.pdf}

\ssk

These notes are at:

\url{http://angg.twu.net/LATEX/2020genericfigures.pdf}

}


\newpage

% «1._the-cat-of-C-sets»  (to ".1._the-cat-of-C-sets")
% (find-books "__cats/__cats.el" "reyes")
% (find-reyeszolfpage  11 "1 The category of C-Sets")
% (find-reyeszolftext  11 "1 The category of C-Sets")

\section*{1. The category of $\C$-Sets}

(Page 12):

%D diagram p.12-rrz
%D 2Dx     100 +25 +25
%D 2D  100 F   X   Y
%D 2D
%D 2D  +20 F'
%D 2D
%D # ren ==>
%D
%D (( F X  --> .plabel= a σ
%D    F F' <-  .plabel= l f
%D    X F' <-- .plabel= r σ.f
%D    X Y   -> .plabel= a Φ
%D ))
%D enddiagram
%D
%D diagram p.12-my
%D 2Dx     100 +20 +30 +20 +30
%D 2D  100 A0  B0  B1  D0  D1
%D 2D  +17                 D3'
%D 2D  +8  A1  B2  B3  D2  D3
%D 2D
%D 2D  +15 A2  C0  C1
%D 2D
%D ren A0 A1 A2    ==> F F' \C^\op
%D ren B0 B1 B2 B3 ==> X(F) Y(F) X(F') Y(F')
%D ren C0 C1       ==> X    Y
%D ren D0 D1 D3'   ==> σ Φ(σ) Φ(σ).f
%D ren D2    D3    ==>    σ.f Φ(σ.f)
%D
%D (( A0 A1 <- .plabel= l f
%D    A2        place
%D    B0 B1 -> .plabel= a Φ_F
%D    B0 B2 -> .plabel= l ().f
%D    B1 B3 -> .plabel= r ().f
%D    B2 B3 -> .plabel= a Φ_{F'}
%D    C0 C1 -> .plabel= a Φ
%D    D0 D1 |-> D1 D3' |->
%D    D0 D2 |-> D2 D3 |->
%D
%D ))
%D enddiagram
%D
$$\pu
  \diag{p.12-rrz}
  \qquad
  \diag{p.12-my}
$$


% (find-latexscan-links "C3" "20210301_fig_1")
% (find-xpdf-page "~/LATEX/2020genericfigures/20210301_fig_1.pdf")
\includegraphics[height=6cm]{2020genericfigures/20210301_fig_1.pdf}
%
% (find-latexscan-links "C3" "20210301_fig_2")
% (find-xpdf-page "~/LATEX/2020genericfigures/20210301_fig_2.pdf")
\includegraphics[height=6cm]{2020genericfigures/20210301_fig_2.pdf}

% (find-latexscan-links "C3" "20210301_fig_3")
% (find-xpdf-page "~/LATEX/2020genericfigures/20210301_fig_3.pdf")
\includegraphics[height=6cm]{2020genericfigures/20210301_fig_3.pdf}




% «1.1._examples-of-C-sets»  (to ".1.1._examples-of-C-sets")
% (find-reyeszolfpage 12 "1.1    Examples of C-Sets")
% (find-reyeszolftext 12 "1.1    Examples of C-Sets")

\section*{1.1. Examples of $\C$-Sets}

% (find-latexscan-links "C3" "20210301_fig_4_incomplete")
% (find-xpdf-page "~/LATEX/2020genericfigures/20210301_fig_4_incomplete.pdf")
\includegraphics[height=4cm]{2020genericfigures/20210301_fig_4_incomplete.pdf}

(Page 18):
%
% (find-reyeszolfpage 18 "whose A-figures are")
% (find-reyeszolftext 18 "whose A-figures are")
%:
%:  V\diagxyto/-->/<200>X
%:  ---------------------
%:      a,b,c
%:
%:      ^p18.V
%:
$$\pu
  \cded{p18.V}
  \qquad
  \text{means}
  \qquad
  \mat{X(V) = \\ \{a,b,c\}}
$$

% «2.2._yoneda-lemma»  (to ".2.2._yoneda-lemma")
\section*{2.2. Yoneda lemma}

% (find-reyeszolfpage 29 "2.2    Yoneda lemma")
% (find-reyeszolftext 29 "2.2    Yoneda lemma")

(Page 29):
%:
%:  F'\diagxyto/-->/<200>h_F
%:  ------------------------
%:  F'\diagxyto/->/<200>F
%:
%:  ^p29.1
%:
$$\pu
  \cded{p29.1}
  \qquad
  \mat{ h_F(F') = (\_{→}F)(F') ≅ \\ (F'→F) }
$$

(Page 35):
%:
%:  F\diagxyto/-->/<200>X
%:  ----------------------
%:  h_F\diagxyto/->/<200>X
%:
%:  ^p35.1
%:
%D diagram yoneda-p35
%D 2Dx     100 +35
%D 2D  100     A1
%D 2D  +20 A2  A3
%D 2D  +20 A4  A5
%D 2D  +15 B0  B1
%D 2D  +15 C1  C2
%D 2D  +20     C3
%D 2D
%D ren    A1 ==>      1
%D ren A2 A3 ==> F  X(F)
%D ren A4 A5 ==> F' X(F')
%D ren B0 B1 ==> \C^\op \Set
%D ren C1 C2 ==> (\_{→}F) (1{→}X\_)
%D ren    C3 ==>           X
%D
%D (( A1 A3  -> .plabel= r \nameof{σ}
%D    A2 A3 |->
%D    A2 A4  <- # .plabel= l φ
%D    A3 A5  ->
%D    A4 A5 |->
%D  # A1 A5  -> .slide= 20pt .plabel= r \nameof{φ(x)}
%D    B0 B1 |-> .plabel= a X
%D    C1 C2  ->
%D    C1 C3  ->
%D    C2 C3 <->
%D ))
%D enddiagram
%D
$$\pu
  \cded{p35.1}
  \qquad
  \mat{ X(F) ≅ \\ (\_{→}F)→X }
  \qquad
  \diag{yoneda-p35}
$$


\GenericWarning{Success:}{Success!!!}  % Used by `M-x cv'


\end{document}

%  __  __       _        
% |  \/  | __ _| | _____ 
% | |\/| |/ _` | |/ / _ \
% | |  | | (_| |   <  __/
% |_|  |_|\__,_|_|\_\___|
%                        
% <make>

 (eepitch-shell)
 (eepitch-kill)
 (eepitch-shell)
# (find-LATEXfile "2019planar-has-1.mk")
make -f 2019.mk STEM=2020genericfigures veryclean
make -f 2019.mk STEM=2020genericfigures pdf

%  ____  _             _         
% |  _ \(_)_   ___   _(_)_______ 
% | | | | \ \ / / | | | |_  / _ \
% | |_| | |\ V /| |_| | |/ /  __/
% |____// | \_/  \__,_|_/___\___|
%     |__/                       
%
% «djvuize»  (to ".djvuize")
% (find-LATEXgrep "grep --color -nH --null -e djvuize 2020-1*.tex")

 (eepitch-shell)
 (eepitch-kill)
 (eepitch-shell)
# (find-fline "~/2020.2-C3/")
# (find-fline "~/LATEX/2020genericfigures/")
# (find-fline "~/bin/djvuize")

cd /tmp/
for i in *.jpg; do echo f $(basename $i .jpg); done

f () { rm -fv $1.png $1.pdf; djvuize $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 1.0" $1.pdf; xpdf $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 0.5" $1.pdf; xpdf $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 0.25" $1.pdf; xpdf $1.pdf }
f () { #cp-fv $1.png $1.pdf       ~/2020genericfigures/
       cp -fv        $1.pdf ~/LATEX/2020genericfigures/
       cat <<%%%
% (find-latexscan-links "C3" "$1")
%%%
}

f 20210301_fig_1
f 20210301_fig_2
f 20210301_fig_3
f 20210301_fig_4_incomplete



% Local Variables:
% coding: utf-8-unix
% ee-tla: "gef"
% End:

