% (find-LATEX "2024emacsconf.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2024emacsconf.tex" :end))
% (defun C () (interactive) (find-LATEXsh "lualatex 2024emacsconf.tex" "Success!!!"))
% (defun D () (interactive) (find-pdf-page      "~/LATEX/2024emacsconf.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2024emacsconf.pdf"))
% (defun e () (interactive) (find-LATEX "2024emacsconf.tex"))
% (defun o () (interactive) (find-LATEX "2024emacsconf.tex"))
% (defun u () (interactive) (find-latex-upload-links "2024emacsconf"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun d0 () (interactive) (find-ebuffer "2024emacsconf.pdf"))
% (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g))
% (defun oe () (interactive) (find-2a '(o) '(e)))
%          (code-eec-LATEX "2024emacsconf")
% (find-pdf-page   "~/LATEX/2024emacsconf.pdf")
% (find-sh0 "cp -v  ~/LATEX/2024emacsconf.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2024emacsconf.pdf /tmp/pen/")
%     (find-xournalpp "/tmp/2024emacsconf.pdf")
%   file:///home/edrx/LATEX/2024emacsconf.pdf
%               file:///tmp/2024emacsconf.pdf
%           file:///tmp/pen/2024emacsconf.pdf
%  http://anggtwu.net/LATEX/2024emacsconf.pdf
% (find-LATEX "2019.mk")
% (find-Deps1-links "Caepro5 Piecewise2 Maxima2")
% (find-Deps1-cps   "Caepro5 Piecewise2 Maxima2")
% (find-Deps1-anggs "Caepro5 Piecewise2 Maxima2")
% (find-MM-aula-links "2024emacsconf" "9" "emacsconf2024" "e24t")

% «.defs»			(to "defs")
% «.defs-T-and-B»		(to "defs-T-and-B")
% «.defs-caepro»		(to "defs-caepro")
% «.defs-pict2e»		(to "defs-pict2e")
% «.defs-maxima»		(to "defs-maxima")
% «.defs-V»			(to "defs-V")
% «.title»			(to "title")
% «.links»			(to "links")
% «.yoneda-on-rings»		(to "yoneda-on-rings")
% «.yoneda-on-rings-2»		(to "yoneda-on-rings-2")
% «.generic»			(to "generic")
% «.download-and-compile»	(to "download-and-compile")



\documentclass[oneside,12pt]{article}
\usepackage[colorlinks,citecolor=DarkRed,urlcolor=DarkRed]{hyperref} % (find-es "tex" "hyperref")
\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-LATEX "dednat7-test1.tex")
%\usepackage{proof}   % For derivation trees ("%:" lines)
\input diagxy        % For 2D diagrams ("%D" lines)
\xyoption{curve}     % For the ".curve=" feature in 2D diagrams
%
\usepackage{edrx21}               % (find-LATEX "edrx21.sty")
\input edrxaccents.tex            % (find-LATEX "edrxaccents.tex")
\input edrx21chars.tex            % (find-LATEX "edrx21chars.tex")
\input edrxheadfoot.tex           % (find-LATEX "edrxheadfoot.tex")
\input edrxgac2.tex               % (find-LATEX "edrxgac2.tex")
%
% (find-es "tex" "geometry")
% (emacsconf2021p 1 "screenshotdimens")
% (emacsconf2021a   "screenshotdimens")
\newdimen\slidewidth
\slidewidth=10.5cm
\slidewidth=11cm
\slidewidth=15cm
%
% (find-es "tex" "geometry")
\usepackage[%a6paper, landscape,
            paperwidth=\slidewidth,
            paperheight=0.625\slidewidth,
            %top=1.5cm, bottom=.25cm, left=1cm, right=1cm, includefoot
            top=1.5cm, bottom=.5cm, left=1cm, right=1cm, includefoot
           ]{geometry}
%\usepackage[a6paper, landscape,
%            top=1.5cm, bottom=.25cm, left=1cm, right=1cm, includefoot
%           ]{geometry}
%
\begin{document}

% «defs»  (to ".defs")
% (find-LATEX "edrx21defs.tex" "colors")
% (find-LATEX "edrx21.sty")

\def\drafturl{http://anggtwu.net/LATEX/2024-2-C9.pdf}
\def\drafturl{http://anggtwu.net/2024.2-C9.html}
\def\drafturl{http://anggtwu.net/emacsconf2024.html}
\def\draftfooter{\tiny \href{\drafturl}{\jobname{}} \ColorBrown{\shorttoday{} \hours}}

% (find-LATEX "2024-1-C2-carro.tex" "defs-caepro")
% (find-LATEX "2024-1-C2-carro.tex" "defs-pict2e")

\catcode`\^^J=10
\directlua{dofile "dednat7load.lua"}  % (find-LATEX "dednat7load.lua")
\directlua{dednat7preamble()}         % (find-angg "LUA/DednatPreamble1.lua")
\directlua{dednat7oldheads()}         % (find-angg "LUA/Dednat7oldheads.lua")

% «defs-T-and-B»  (to ".defs-T-and-B")
\long\def\ColorDarkOrange#1{{\color{orange!90!black}#1}}
\def\T(Total: #1 pts){{\bf(Total: #1)}}
\def\T(Total: #1 pts){{\bf(Total: #1 pts)}}
\def\T(Total: #1 pts){\ColorRed{\bf(Total: #1 pts)}}
\def\B       (#1 pts){\ColorDarkOrange{\bf(#1 pts)}}

% «defs-caepro»  (to ".defs-caepro")
%L --dofile "Caepro5.lua"              -- (find-angg "LUA/Caepro5.lua" "LaTeX")
\def\Caurl   #1{\expr{Caurl("#1")}}
\def\Cahref#1#2{\href{\Caurl{#1}}{#2}}
\def\Ca      #1{\Cahref{#1}{#1}}

% «defs-pict2e»  (to ".defs-pict2e")
%L --dofile "Piecewise2.lua"           -- (find-LATEX "Piecewise2.lua")
%L --dofile "Escadas1.lua"           -- (find-LATEX "Escadas1.lua")
\def\pictgridstyle{\color{GrayPale}\linethickness{0.3pt}}
\def\pictaxesstyle{\linethickness{0.5pt}}
\def\pictnaxesstyle{\color{GrayPale}\linethickness{0.5pt}}
\celllower=2.5pt

% «defs-maxima»  (to ".defs-maxima")
%L --dofile "Maxima2.lua"              -- (find-angg "LUA/Maxima2.lua")
\pu

% «defs-V»  (to ".defs-V")
%L --- See: (find-angg "LUA/MiniV1.lua" "problem-with-V")
%L --V = MiniV
%L --v = V.fromab
\pu

\def\ph{\phantom}

\def\respcomp{\mathsf{respcomp}}
\def\respids {\mathsf{respids}}
\def\sqcond  {\mathsf{sqcond}}
\def\assoc   {\mathsf{assoc}}
\def\idL     {\mathsf{idL}}
\def\idR     {\mathsf{idR}}
\def\univ    {\mathsf{univ}}
\def\Ran     {\mathsf{Ran}}

\def\sfC  {\mathsf{C}}
\def\sfSet{\mathsf{Set}}
\def\Ring {\mathbf{Ring}}
\def\nameof#1{\ulcorner#1\urcorner}
\def\catK {\mathbf{K}}
\def\Dn   {\Downarrow}

\def\veq{\rotatebox{90}{$=$}}
\def\liml{\underleftarrow {\lim}{}}
\def\limr{\underrightarrow{\lim}{}}
\def\veq{\rotatebox{90}{$=$}}

\def\Yzero    {\mathsf{Y0}}
\def\Yzeroplus{\mathsf{Y0^+}}
\def\Yone     {\mathsf{Y1}}
\def\Ytwo     {\mathsf{Y2}}
\def\Ythree   {\mathsf{Y3}}
\def\Yfour    {\mathsf{Y4}}
\def\Yfive    {\mathsf{Y5}}

\def\origphi{\phi}

\def\AProofOf   #1{\llangle#1\rrangle}
\def\AllProofsOf#1{\llbracket#1\rrbracket}

\def\DONE{(DONE)}
\def\DONE{}


%  _____ _ _   _                               
% |_   _(_) |_| | ___   _ __   __ _  __ _  ___ 
%   | | | | __| |/ _ \ | '_ \ / _` |/ _` |/ _ \
%   | | | | |_| |  __/ | |_) | (_| | (_| |  __/
%   |_| |_|\__|_|\___| | .__/ \__,_|\__, |\___|
%                      |_|          |___/      
%
% «title»  (to ".title")
% (emacsconf2024p 1 "title")
% (emacsconf2024a   "title")
% (2024panic-teresopolisp 1 "title")
% (2024panic-teresopolisa   "title")

\thispagestyle{empty}

\begin{center}

\vspace*{1.2cm}

{\bf \large Emacs, eev, and Maxima -- Now!}

\msk

Eduardo Ochs % - RCN/PURO/UFF

December 7, 2024

\msk

{\scriptsize

\url{http://anggtwu.net/emacsconf2024.html}

\url{https://emacsconf.org/2024/talks/maxima/}

}



\end{center}

\newpage

% «links»  (to ".links")
% (emacsconf2024p 2 "links")
% (emacsconf2024a   "links")

{\bf Links}

\scalebox{0.6}{\def\colwidth{16cm}\firstcol{

% (find-math-b-links "2022-md" "2022on-the-missing")
% (find-TH "math-b" "2022-md")
%    http://anggtwu.net/math-b.html\#2022-md
\par \url{http://anggtwu.net/math-b.html\#2022-md}

\ssk

% (find-books "__cats/__cats.el" "riehl")
\par \url{http://www.math.jhu.edu/~eriehl/}
\par \url{http://www.math.jhu.edu/~eriehl/context.pdf}



}\anothercol{
}}

\newpage

\newpage

% «yoneda-on-rings»  (to ".yoneda-on-rings")
% (emacsconf2024p 3 "yoneda-on-rings")
% (emacsconf2024a   "yoneda-on-rings")
% (misp 49 "representable-functors")
% (misa    "representable-functors")

{\bf Yoneda on rings}

%D diagram Y5-rings
%D 2Dx     100    +25 +20 +20   +30    +30
%D 2D  100 D0 <-| D1  F0  G0           A1  
%D 2D      |       |   |   |            |  
%D 2D  +20 D2 |-> D3  F1  G1    A2 |-> A3  
%D 2D                          
%D 2D  +15 E0 === E1            B0 --> B1  
%D 2D                          
%D 2D  +15                      C0 --> C1
%D 2D                               \   |
%D 2D  +20                             C2  
%D 2D
%D ren    A1 ==>                1
%D ren A2 A3 ==>       \Z[x]   U\Z[x]
%D ren B0 B1 ==> \Ring         \Set
%D ren C0 C2 ==> \Ring(\Z[x],-) U
%D ren D0 D1 ==> FA A
%D ren D2 D3 ==> B UB
%D ren E0 E1 ==> \Ring \Set
%D ren F0 F1 ==> A UFA
%D ren G0 G1 ==> 1 U\Z[x]
%D
%D (( A1 A3  -> .plabel= r \sm{\nameof{x}\\\univ}
%D    A2 A3 |->
%D    B0 B1  -> .plabel= a U
%D    C0 C2 <-> # .plabel= l β
%D    
%D    D0 D1 <-|
%D    D0 D2  ->
%D    D1 D3  ->
%D    D2 D3 |->
%D    D0 D3 harrownodes nil 20 nil <->
%D    E0 E1 <-  sl^ .plabel= a F
%D    E0 E1  -> sl_ .plabel= b U
%D    F0 F1  -> .plabel= r η_A
%D    G0 G1  -> .plabel= r η_1
%D ))
%D enddiagram
%
\pu

\scalebox{0.85}{\def\colwidth{6.5cm}\firstcol{

{}

This is the example (iv) in p.52 of Emily Riehl's
``{\sl Category Theory in Context}'':

\msk

The functor $U:\Ring→\Set$ is represented by the unital
  ring $\Z[x]$, the polynomial ring in one variable with integer
  coefficients. A unital ring homomorphism $Z[x]→R$ is uniquely
  determined by the image of $x$; put another way, $\Z[x]$ is the {\sl
    free unital ring on a single generator}.

}\anothercol{

% The diagram below is a good way to visualize that:
%
$$\scalebox{0.7}{$\diag{Y5-rings}$}
$$

}}

\newpage

% «yoneda-on-rings-2»  (to ".yoneda-on-rings-2")
% (emacsconf2024p 4 "yoneda-on-rings-2")
% (emacsconf2024a   "yoneda-on-rings-2")

{\bf Yoneda on rings}

\vspace*{0.1cm}

$$\scalebox{1.0}{$\diag{Y5-rings}$}
$$


\newpage


% «generic»  (to ".generic")
% (emacsconf2024p 5 "generic")
% (emacsconf2024a   "generic")
% (misp 41 "basic-example-full")
% (misa    "basic-example-full")

%D diagram Basic-Example
%D 2Dx     100    +40
%D 2D  100        A1
%D 2D              |
%D 2D  +20 A2 |-> A3
%D 2D
%D 2D  +15 B0 --> B1
%D 2D
%D 2D  +15 C0 --> C1
%D 2D          \   |
%D 2D  +20        C2
%D 2D
%D ren    A1 ==>      A
%D ren A2 A3 ==>  C  RC
%D ren B0 B1 ==>  \catB \catA
%D ren C0 C1 C2 ==> \catB(C,-) \catA(A,R-) ?
%D
%D (( A1 A3  -> .plabel= r η
%D    A2 A3 |->
%D
%D    B0 B1  -> .plabel= a R\phantom{mmm}
%D
%D    C0 C1 -> .plabel= b α
%D  # C0 C2 -> .plabel= l \sm{ψ\\\text{(iso)}}
%D  # C1 C2 <->
%D
%D    C0 C1 midpoint A1 A3 midpoint <-> .curve= ^15pt
%D ))
%D enddiagram
%
\pu

\vspace*{-0.5cm}

$$\scalebox{0.6}{$
  \diag{Basic-Example}
  \qquad
  \begin{array}{rl}
    & \catA \text{ is a category}, \\
    & \catB \text{ is a category}, \\
    & R:\catB \to \catA, \\
    & A ∈ \catA, \\
    & C ∈ \catB, \\
    & η:A→RD, \\
      [5pt]
    & \catB(C,-)    :  \catB → \Set,   \\
    & \catB(C,-)_0  := λD.\catB(C,D),  \\
    & \catB(C,-)_1  := λg.λf.\;g∘f,      \\
      [5pt]
    & \catA(A,R-)   : \catA → \Set,    \\
    & \catA(A,R-)_0 := λD.\catA(A,RD), \\
    & \catA(A,R-)_1 := λg.λh.Rg∘h,     \\
      [5pt]
    & α : \catB(C,-) → \catA(A,R-), \\
      [5pt]
    & (η↦α_0) := λη.λD.λf.\;Rf∘η, \\
    & (α↦η)   := λα.\; αC(\id_C), \\
      [5pt]
    & \text{or:} \\
    & α_0 := λD.λf.Rf∘η, \\
    & η := αC(\id_C). \\
  \end{array}
  $}
$$

\vspace*{-5cm}





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

\end{document}

% «download-and-compile»  (to ".download-and-compile")
% (emacsconf2024a "download-and-compile")

 (eepitch-shell)
 (eepitch-kill)
 (eepitch-shell)
# Test the .zip.
# The e-script below downloads, unpacks and compiles the .zip in /tmp/edrx-latex/
#
rm -rfv /tmp/2024emacsconf.zip
rm -rfv /tmp/edrx-latex/
cd /tmp/
wget http://anggtwu.net/LATEX/2024emacsconf.zip
# cp -v ~/LATEX/2024emacsconf.zip .
mkdir    /tmp/edrx-latex/
unzip -d /tmp/edrx-latex/ /tmp/2024emacsconf.zip
cd       /tmp/edrx-latex/
lualatex 2024emacsconf.tex
# (find-fline    "/tmp/edrx-latex/")
# (find-pdf-page "/tmp/edrx-latex/2024emacsconf.pdf")
# (find-pdf-text "/tmp/edrx-latex/2024emacsconf.pdf")



% (find-pdfpages2-links "~/LATEX/" "2024emacsconf")


% Local Variables:
% coding: utf-8-unix
% ee-tla: "e24t"
% ee-tla: "emacsconf2024"
% End:
