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

% «.reflexivity»	(to "reflexivity")

\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")



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

Notes on Lawvere's

``Equality in hyperdoctrines and comprehension schema as an adjoint
functor'' (1970)

\url{https://github.com/mattearnshaw/lawvere/blob/master/pdfs/1970-equality-in-hyperdoctrines-and-comprehension-schema-as-an-adjoint-functor.pdf}

\ssk

These notes are at:

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

}

\bsk
\bsk


(Page 5):

% «reflexivity»  (to ".reflexivity")
% (leqp 1 "reflexivity")
% (leq    "reflexivity")
% (hypp 10 "equahyp-p5")
% (hyp     "equahyp-p5")
% (find-books "__cats/__cats.el" "lawvere-equahyp")
% (find-lawvereequahyppage 5 "reflexivity")
% (find-lawvereequahyptext 5 "reflexivity")

%D diagram ??
%D 2Dx     100 +35 +20 +10    +30 +30
%D 2D  100 A0  A1  A1= A1R    C0  C1
%D 2D
%D 2D  +25 A2  A3             C2  C3
%D 2D
%D 2D  +15 B0  B1             D0  D1
%D 2D
%D ren A0 A1 A1= A1R ==> 1_X 1_XΣ(Xδ) = Θ_X
%D ren A2 A3         ==> (Xδ)·Θ_X Θ_X
%D ren B0 B1         ==> X X{×}X
%D
%D ren C0 C1 C2 C3   ==> ⊤ x{=}x' x{=}x x{=}x'
%D ren D0 D1         ==> X X{×}X
%D
%D (( A0 A1 |-> A1= place A1R place
%D    A0 A2 -> .plabel= l \text{reflexivity}
%D    A1 A3 -> .plabel= r \id
%D    A0 A3 harrownodes nil 20 nil <-|
%D    A2 A3 <-|
%D    B0 B1 -> .plabel= a Xδ
%D ))
%D (( C0 C1 |->
%D    C0 C2 -> .plabel= l \text{reflexivity}
%D    C1 C3 -> .plabel= r \id
%D    C0 C3 harrownodes nil 20 nil <-|
%D    C2 C3 <-|
%D    D0 D1 -> .plabel= a Xδ
%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-equahyp veryclean
make -f 2019.mk STEM=2020lawvere-equahyp pdf

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