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% (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: