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

\def\Pb{\mathsf{Pb}}
\def\tn#1{{\ton{#1}}}



%D diagram pbdef
%D 2Dx     100 +30
%D 2D  100 A0
%D 2D
%D 2D  +30 A2  A3
%D 2D
%D 2D  +30 A4  A5
%D 2D
%D ren A0 ==> ∂_0(k_0)=∂_0(k_1)
%D ren A2 A3 ==> \Pb(f,g) ·
%D ren A4 A5 ==> · ·
%D
%D (( A0 A2 -> .plabel= m 〈k_0,k_1〉_{f,g}
%D    A0 A3 -> .plabel= r k_1
%D    A2 A3 -> .plabel= b π_1^{f,g}
%D    A2 A4 -> .plabel= m π_0^{f,g}
%D    A3 A5 -> .plabel= r g
%D    A4 A5 -> .plabel= a f
%D    A0 A4 -> .slide= -10pt .curve= _20pt .plabel= l k_0
%D    A2 relplace 8 8 \pbsymbol{7}
%D ))
%D enddiagram
%D
%D diagram proddef
%D 2Dx     100 +30
%D 2D  100 A0
%D 2D
%D 2D  +30 A2  A3
%D 2D
%D 2D  +30 A4  A5
%D 2D
%D ren A0    ==> C
%D ren A2 A3 ==> A{×}B B
%D ren A4 A5 ==> A 1
%D
%D (( A0 A2 -> .plabel= m 〈f,g〉_{A,B}
%D    A0 A3 -> .plabel= r g
%D    A2 A3 -> .plabel= b π_1^{A,B}
%D    A2 A4 -> .plabel= m π_0^{A,B}
%D    A3 A5 -> .plabel= r !_B
%D    A4 A5 -> .plabel= a !_A
%D    A0 A4 -> .slide= -5pt .curve= _20pt .plabel= l f
%D    A2 relplace 7 7 \pbsymbol{7}
%D ))
%D enddiagram
%D
$$\pu
  \diag{pbdef}
  \qquad
  \diag{proddef}
$$


%D diagram ic0
%D 2Dx     100 +20 +20 +20
%D 2D  100 A0 ---> A1
%D 2D      | \        \
%D 2D  +20 |   A2 ---> A3
%D 2D      v   |
%D 2D  +20 A4 -|-> A5
%D 2D        \ v
%D 2D  +20     A6
%D 2D
%D ren A0 A1 ==> Γ_2=\Pb(δ_1,δ_0) Γ_1
%D ren A2 A3 ==> Γ_1 Γ_0
%D ren A4 A5 ==> Γ_1 Γ_0
%D ren A6    ==> Γ_0
%D
%D (( # Horizontal arrows:
%D    A0 A1 |-> .plabel= a π_1
%D    A2 A3 |-> .PLABEL= ^<>(0.1) δ_1
%D    A4 A5 |-> .PLABEL= ^<>(0.1) δ_1
%D    # Vertical arrows:
%D    A0 A4 |-> .plabel= l π_0
%D    A1 A5 |-> .PLABEL= _<>(0.1) δ_0
%D    A2 A6 |-> .PLABEL= _<>(0.1) δ_0
%D    # Diagonal arrows:
%D    A0 A2 |-> .plabel= a ◻
%D    A1 A3 |-> .plabel= r δ_1
%D    A4 A6 |-> .plabel= l δ_0
%D ))
%D enddiagram
%D
%D diagram ic1
%D 2Dx     100 +20 +20 +20
%D 2D  100 A0 ---> A1
%D 2D      | \        \
%D 2D  +20 |   A2 ---> A3
%D 2D      v   |
%D 2D  +20 A4 -|-> A5
%D 2D        \ v
%D 2D  +20     A6
%D 2D
%D ren A0 A1 ==> (A\tn{f}B\tn{g}C) (B\tn{g}C)
%D ren A2 A3 ==> (A\tn{g∘f}C)  C
%D ren A4 A5 ==> (A\tn{f}B)         B
%D ren A6    ==> A
%D
%D (( # Horizontal arrows:
%D    A0 A1 |-> .plabel= a π_1
%D    A2 A3 |-> .PLABEL= ^<>(0.1) δ_1
%D    A4 A5 |-> .PLABEL= ^<>(0.1) δ_1
%D    # Vertical arrows:
%D    A0 A4 |-> .plabel= l π_0
%D    A1 A5 |-> .PLABEL= _<>(0.1) δ_0
%D    A2 A6 |-> .PLABEL= _<>(0.1) δ_0
%D    # Diagonal arrows:
%D    A0 A2 |-> .plabel= a ◻
%D    A1 A3 |-> .plabel= r δ_1
%D    A4 A6 |-> .plabel= l δ_0
%D ))
%D enddiagram
%D
%D diagram ic2
%D 2Dx     100 +20 +20 +20
%D 2D  100 A0 ---> A1
%D 2D      | \        \
%D 2D  +20 |   A2 ---> A3
%D 2D      v   |
%D 2D  +20 A4 -|-> A5
%D 2D        \ v
%D 2D  +20     A6
%D 2D
%D ren A0 A1 ==> (f,g) g
%D ren A2 A3 ==> g∘f  C
%D ren A4 A5 ==> f   B
%D ren A6    ==> A
%D
%D (( # Horizontal arrows:
%D    A0 A1 |-> .plabel= a π_1
%D    A2 A3 |-> .PLABEL= ^<>(0.1) δ_1
%D    A4 A5 |-> .PLABEL= ^<>(0.1) δ_1
%D    # Vertical arrows:
%D    A0 A4 |-> .plabel= l π_0
%D    A1 A5 |-> .PLABEL= _<>(0.1) δ_0
%D    A2 A6 |-> .PLABEL= _<>(0.1) δ_0
%D    # Diagonal arrows:
%D    A0 A2 |-> .plabel= a ◻
%D    A1 A3 |-> .plabel= r δ_1
%D    A4 A6 |-> .plabel= l δ_0
%D ))
%D enddiagram
%D
$$\pu
  \diag{ic0}
  \quad
  \diag{ic1}
  \quad
  \diag{ic2}
$$


%D diagram pbdef
%D 2Dx     100 +20
%D 2D  100 A0
%D 2D
%D 2D  +20 A2  A3
%D 2D
%D 2D  +20 A4  A5
%D 2D
%D # ren ==>
%D
%D (( A0 A2 ->
%D    A0 A3 ->
%D    A2 A3 ->
%D    A2 A4 ->
%D    A3 A5 ->
%D    A4 A5 ->
%D    A0 A4 -> .curve= _20pt
%D ))
%D enddiagram
%D
$$\pu
  \diag{pbdef}
$$





\end{document}

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

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

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