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

\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-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")

\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{SpringGreen4}#1}}
\long\def\ColorGreen #1{{\color{SpringGreenDark}#1}}
\long\def\ColorGray  #1{{\color{GrayLight}#1}}
\long\def\ColorGray  #1{{\color{black!30!white}#1}}

\def\univ    {\mathsf{univ}}

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

Notes on Mario Cáccamo's PhD thesis, available at:

\url{http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1.7460}

\ssk

These notes are at:

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

See:

\url{http://angg.twu.net/LATEX/2020favorite-conventions.pdf}

\url{http://angg.twu.net/math-b.html\#favorite-conventions}


}


% (find-books "__cats/__cats.el" "caccamo-phd")
% (find-caccamophdpage (+ 16   5) "1.3. Functoriality and Naturality")
% (find-caccamophdtext (+ 16   5) "1.3. Functoriality and Naturality")
% (find-caccamophdpage (+ 16 5) "place-holders")
% (find-caccamophdtext (+ 16 5) "place-holders")
% (find-caccamophdpage (+ 16 7) "contravariant Yoneda")
% (find-caccamophdtext (+ 16 7) "contravariant Yoneda")
% (find-caccamophdpage (+ 16 21) "bookkeeping")
% (find-caccamophdtext (+ 16 21) "bookkeeping")

% (find-caccamophdpage (+ 16  21) "2.2.4 Preservation of Limits")
% (find-caccamophdpage (+ 16  21) "2.3 Adjunctions")
% (find-caccamophdpage (+ 16  24) "2.3.1 Examples of Adjunctions")
% (find-caccamophdpage (+ 16  27) "3 Ends and Coends")
% (find-caccamophdpage (+ 16  27) "3.1 Dinatural Transformations")
% (find-caccamophdpage (+ 16  30) "3.1.1 Dinaturality generalises naturality")
% (find-caccamophdpage (+ 16  30) "3.1.2 Wedges")
% (find-caccamophdpage (+ 16  31) "3.1.3 Examples")
% (find-caccamophdpage (+ 16  33) "3.2 Ends")
% (find-caccamophdpage (+ 16  34) "3.2.1 Limits are Ends")
% (find-caccamophdpage (+ 16  34) "3.2.2 Ends are Limits")
% (find-caccamophdpage (+ 16  35) "3.2.3 Ends in Set")
% (find-caccamophdpage (+ 16  35) "3.2.4 (Di)Naturality Formula")
% (find-caccamophdpage (+ 16  36) "3.2.5 Iterated Ends: Fubini")
% (find-caccamophdpage (+ 16  38) "3.2.6 Ends in Functor Categories")
% (find-caccamophdpage (+ 16  39) "3.3 Coends")





% (favp 40 "representable-functors")
% (fav     "representable-functors")

%D diagram univ-arrows-univ-elts
%D 2Dx     100    +40   +50    +40
%D 2D  100        A1           D1 
%D 2D              |            | 
%D 2D  +20 A2 |-> A3    D2 |-> D3 
%D 2D      |       |    |       | 
%D 2D  +20 A4 |-> A5    D4 |-> D5 
%D 2D                             
%D 2D  +15 B0 --> B1    E0 --> E1 
%D 2D                             
%D 2D  +15 C0 --> C1    F0 --> F1 
%D 2D          \   |        \   | 
%D 2D  +20        C2           F2 
%D 2D
%D ren    A1 ==>      A
%D ren A2 A3 ==>  C  RC
%D ren A4 A5 ==>  D  RD
%D ren B0 B1 ==>  \catB \catA
%D ren C0 C1 C2 ==> \catB(C,-) \catA(A,R-) ?
%D
%D ren    D1 ==>      1
%D ren D2 D3 ==>  C  RC
%D ren D4 D5 ==>  D  RD
%D ren E0 E1 ==>  \catB \Set
%D ren F0 F1 F2 ==> \catB(C,-) \Set(1,R-) R
%D
%D (( A1 A3  -> .plabel= r \sm{η\\\univ}
%D    A2 A3 |->
%D    A2 A4  -> .plabel= l f
%D    A3 A5  -> .plabel= r Rf
%D    A2 A5 harrownodes nil 20 nil |->
%D    A4 A5 |->
%D    A1 A5  -> .slide= 25pt .plabel= r h
%D
%D    B0 B1  -> .plabel= a R\phantom{mmm}
%D
%D    C0 C1 <-> .plabel= b T
%D    C0 C1 midpoint A1 A3 midpoint <-> .curve= ^15pt
%D ))
%D (( D1 D3  -> .plabel= r \sm{η\\\univ}
%D    D2 D3 |->
%D    D2 D4  -> .plabel= l f
%D    D3 D5  -> .plabel= r Rf
%D    D2 D5 harrownodes nil 20 nil |->
%D    D4 D5 |->
%D    D1 D5  -> .slide= 25pt .plabel= r h
%D
%D    E0 E1  -> .plabel= a R\phantom{mmm}
%D
%D    F0 F1 <-> .plabel= b T
%D    F0 F2 <-> .plabel= l T'
%D    F1 F2 <->
%D
%D    F0 F1 midpoint D1 D3 midpoint <-> .curve= ^15pt
%D ))
%D enddiagram
%
$$\pu
  \diag{univ-arrows-univ-elts}
$$



\end{document}

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

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

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