Warning: this is an htmlized version! The original is here, and the conversion rules are here.
% (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 v () (interactive) (find-2a '(e) '(d)) (g))
% (find-sh0 "cp -v  ~/LATEX/2020lawvere-adjfo.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2020lawvere-adjfo.pdf /tmp/pen/")
% (find-LATEX "2019.mk")

% «.title»	(to "title")

\documentclass[oneside,12pt]{article}
\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 edrxgac2.tex               % (find-LATEX "edrxgac2.tex")
%
% (find-es "tex" "geometry")
\begin{document}

\catcode\^^J=10

% «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:

}

% (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}

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%
% <make>

* (eepitch-shell)
* (eepitch-kill)
* (eepitch-shell)
# (find-LATEXfile "2019planar-has-1.mk")

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