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

% «.title»	(to "title")

\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")


% «title»  (to ".title")

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

Notes on Lawvere's ``Adjointness in Foundations'' (1969):

\url{http://www.tac.mta.ca/tac/reprints/articles/16/tr16abs.html}

\url{http://www.tac.mta.ca/tac/reprints/articles/16/tr16.pdf}

\ssk

These notes are at:

\url{http://angg.twu.net/LATEX/2020lawvere-adjfo.pdf}

}



% (find-books "__cats/__cats.el" "lawvere-adjfo")
% (find-lawvereadjfopage 11 "A hyperdoctrine shall consist of")
% (find-lawvereadjfotext 11 "A hyperdoctrine shall consist of")

% (find-books "__cats/__cats.el" "avery")
% Tom Avery: Structure and Semantics


\section*{3. Cartesian-closed Categories and Hyperdoctrines}


(Page 11):

A hyperdoctrine shall consist of at least the following four data...


%D diagram ??
%D 2Dx     100 +45 +45
%D 2D  100 A0  A1  
%D 2D
%D 2D  +20 A2  A3
%D 2D
%D 2D  +20 A4  A5  
%D 2D
%D 2D  +20 B0  B1
%D 2D
%D 2D  +20 C0  C1  
%D 2D
%D ren A0 A1 ==> φ φΣf
%D ren A2 A3 ==> f·ψ ψ
%D ren A4 A5 ==> σ σΠf
%D ren B0 B1 ==> P(X) P(Y)
%D ren C0 C1 ==> X Y
%D (( A0 A1  A2 A3  A4 A5
%D    @ 0 @ 1 |->
%D    @ 0 @ 2 -> @ 1 @ 3 ->
%D    @ 0 @ 3 harrownodes nil 20 nil <->
%D    @ 2 @ 3 <-|
%D    @ 2 @ 4 -> @ 3 @ 5 ->
%D    @ 0 @ 3 harrownodes nil 20 nil <->
%D    @ 4 @ 5 |->
%D ))
%D ((
%D     B0 B1 -> sl^^ .plabel= a (\,)Σf
%D     B0 B1 <-      .plabel= m f·(\,)
%D     B0 B1 -> sl__ .plabel= b (\,)Πf
%D     C0 C1 ->      .plabel= a f
%D ))
%D enddiagram
%D
$$\pu
  \diag{??}
$$




\end{document}

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

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

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

