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% (find-angg "LATEX/2019jacobs.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2019jacobs.tex"))
% (defun d () (interactive) (find-pdf-page "~/LATEX/2019jacobs.pdf"))
% (defun b () (interactive) (find-zsh "bibtex 2019jacobs; makeindex 2019jacobs"))
% (defun e () (interactive) (find-LATEX "2019jacobs.tex"))
% (defun u () (interactive) (find-latex-upload-links "2019jacobs"))
% (find-xpdfpage "~/LATEX/2019jacobs.pdf")
% (find-sh0 "cp -v ~/LATEX/2019jacobs.pdf /tmp/")
% (find-sh0 "cp -v ~/LATEX/2019jacobs.pdf /tmp/pen/")
% file:///home/edrx/LATEX/2019jacobs.pdf
% file:///tmp/2019jacobs.pdf
% file:///tmp/pen/2019jacobs.pdf
% http://angg.twu.net/LATEX/2019jacobs.pdf
\documentclass[oneside]{book}
\usepackage[colorlinks]{hyperref} % (find-es "tex" "hyperref")
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{pict2e}
\usepackage[x11names,svgnames]{xcolor} % (find-es "tex" "xcolor")
%\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")
%
\begin{document}
\catcode`\^^J=10
\directlua{dofile "dednat6load.lua"} % (find-LATEX "dednat6load.lua")
% %L dofile "edrxtikz.lua" -- (find-LATEX "edrxtikz.lua")
% %L dofile "edrxpict.lua" -- (find-LATEX "edrxpict.lua")
% \pu
% (find-books "__cats/__cats.el" "jacobs")
% (find-jacobspage (+ 20 219) "4. First order predicate logic")
% (find-jacobspage (+ 20 221) "4.1. Signatures, connectives and quantifiers")
% (find-jacobspage (+ 20 232) "4.2. Fibrations for first order predicate logic")
% (find-jacobspage (+ 19 610) "10.4.2." "comprehension category")
% (find-jacobspage (+ 19 614) "some important examples of (full) comprehension")
% (find-jacobspage (+ 19 616) "10.4.7." "comprehension category with unit")
\def\AAA{AAA}
\def\BBB{BBB}
%
%D diagram triangleidentityadjunctiondiagram1
%D 2Dx 100 +25
%D 2D 100 A1 A2
%D 2D +25 A3 A4
%D 2D
%D
%D
%D ((
%D ren A1 A2 A3 A4 ==> \AAA \BBB \AAA \BBB
%D
%D # 1cells
%D
%D
%D A1 A2 -> .plabel= a G
%D A1 A3 =
%D A2 A4 =
%D A3 A4 -> .plabel= b G
%D A2 A3 -> .plabel= m F
%D
%D
%D
%D # 1cells
%D
%D
%D
%D # 2cells
%D
%D A2 A3 harrownodes 10 18 nil <= .slide= -10pt .plabel= a \eta
%D A2 A3 harrownodes -5 18 nil <= .slide= 10pt .plabel= a \varepsilon
%D
%D
%D ))
%D enddiagram
%D
\pu
\begin{equation*}
\diag{triangleidentityadjunctiondiagram1}
\end{equation*}
%
%D diagram identityofmonad
%D 2Dx 100 +25 +25
%D 2D 100 T1 T2 T3
%D 2D +25 T4
%D 2D
%D
%D
%D ((
%D T1 .tex= T
%D T2 .tex= T
%D T3 .tex= T
%D T4 .tex= T
%D
%D # 1cells
%D
%D T1 T2 -> .plabel= a \id_T\ast\eta
%D T3 T2 -> .plabel= a \eta\ast\id_T
%D T2 T4 -> .plabel= m \mu
%D T1 T4 =
%D T3 T4 =
%D
%D
%D # 2cells
%D
%D ))
%D enddiagram
%D
\pu
%
%D diagram associativityofmonad
%D 2Dx 100 +25
%D 2D 100 T1 T2
%D 2D +25 T4 T3
%D 2D
%D
%D
%D ((
%D T1 .tex= T^3
%D T2 .tex= T^2
%D T3 .tex= T^2
%D T4 .tex= T
%D
%D # 1cells
%D
%D T1 T2 -> .plabel= a \mu\ast\id_T
%D T1 T4 -> .plabel= a \id_T\ast\mu
%D T4 T3 -> .plabel= b \mu
%D T2 T3 -> .plabel= r c
%D
%D
%D # 2cells
%D
%D ))
%D enddiagram
%D
\pu
\begin{equation*}
\diag{identityofmonad}\quad \diag{associativityofmonad}
\end{equation*}
%
%D diagram identityofmonad
%D 2Dx 100 +25 +25
%D 2D 100 T1 T2 T3
%D 2D +25 T4
%D 2D
%D
%D
%D ((
%D T1 .tex= T
%D T2 .tex= T
%D T3 .tex= T
%D T4 .tex= T
%D
%D # 1cells
%D
%D T1 T2 -> .plabel= a \id_T\ast\eta
%D T3 T2 -> .plabel= a \eta\ast\id_T
%D T2 T4 -> .plabel= m \mu
%D T1 T4 =
%D T3 T4 =
%D
%D
%D # 2cells
%D
%D ))
%D enddiagram
%D
\pu
%
%D diagram associativityofmonad
%D 2Dx 100 +25
%D 2D 100 T1 T2
%D 2D +25 T4 T3
%D 2D
%D
%D
%D ((
%D T1 .tex= T^3
%D T2 .tex= T^2
%D T3 .tex= T^2
%D T4 .tex= T
%D
%D # 1cells
%D
%D T1 T2 -> .plabel= a \mu\ast\id_T
%D T1 T4 -> .plabel= a \id_T\ast\mu
%D T4 T3 -> .plabel= l \mu
%D T2 T3 -> .plabel= r \mu
%D
%D
%D # 2cells
%D
%D ))
%D enddiagram
%D
\pu
\begin{equation*}
\diag{identityofmonad}\quad \diag{associativityofmonad}
\end{equation*}
%
%D diagram identityofmonad
%D 2Dx 100 +25 +25
%D 2D 100 T1 T2 T3
%D 2D +25 T4
%D 2D
%D
%D
%D ((
%D T1 .tex= T
%D T2 .tex= T^2
%D T3 .tex= T
%D T4 .tex= T
%D
%D # 1cells
%D
%D T1 T2 -> .plabel= a \id_T\ast\eta
%D T3 T2 -> .plabel= a \eta\ast\id_T
%D T2 T4 -> .plabel= m \mu
%D T1 T4 =
%D T3 T4 =
%D
%D
%D # 2cells
%D
%D ))
%D enddiagram
%D
\pu
%
%D diagram associativityofmonad
%D 2Dx 100 +25
%D 2D 100 T1 T2
%D 2D +25 T3 T4
%D 2D
%D
%D
%D ((
%D T1 .tex= T^3
%D T2 .tex= T^2
%D T3 .tex= T^2
%D T4 .tex= T
%D
%D # 1cells
%D
%D T1 T2 -> .plabel= a \mu\ast\id_T
%D T1 T3 -> .plabel= a \id_T\ast\mu
%D T3 T4 -> .plabel= l \mu
%D T2 T4 -> .plabel= r \mu
%D
%D
%D # 2cells
%D
%D ))
%D enddiagram
%D
%D ren T1 T2 T2 T4 ==> T^3 T^2 T^2 T
\pu
\begin{equation*}
\diag{identityofmonad}\quad \diag{associativityofmonad}
\end{equation*}
\end{document}
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