% (find-LATEX "2021other-bijections.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2021other-bijections.tex" :end))
% (defun C () (interactive) (find-LATEXSH "lualatex 2021other-bijections.tex" "Success!!!"))
% (defun D () (interactive) (find-pdf-page      "~/LATEX/2021other-bijections.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2021other-bijections.pdf"))
% (defun e () (interactive) (find-LATEX "2021other-bijections.tex"))
% (defun u () (interactive) (find-latex-upload-links "2021other-bijections"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g))
% (defun d0 () (interactive) (find-ebuffer "2021other-bijections.pdf"))
%          (code-eec-LATEX "2021other-bijections")
% (find-pdf-page   "~/LATEX/2021other-bijections.pdf")
% (find-sh0 "cp -v  ~/LATEX/2021other-bijections.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2021other-bijections.pdf /tmp/pen/")
%   file:///home/edrx/LATEX/2021other-bijections.pdf
%               file:///tmp/2021other-bijections.pdf
%           file:///tmp/pen/2021other-bijections.pdf
% http://angg.twu.net/LATEX/2021other-bijections.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")
%\input 2017planar-has-defs.tex    % (find-LATEX "2017planar-has-defs.tex")
%
%\usepackage[backend=biber,
%   style=alphabetic]{biblatex}            % (find-es "tex" "biber")
%\addbibresource{catsem-slides.bib}        % (find-LATEX "catsem-slides.bib")
%
% (find-es "tex" "geometry")
\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


\def\Downs {\mathcal{D}}
\def\Ddp   {\Downs({↓}p)}
\def\singp {\{p\}}
\def\dnp   {{↓}p}
\def\dnpo  {{↓}p∖\{p\}}
\def\setofsc#1#2{\{\,#1\;:\;#2\,\}}
\def\nuc   {(·)^*}
\def\clop  {\ovl{(·)}}
\def\Nucs  {\mathsf{Nucs}}
\def\GrTops{\mathsf{GrTops}}
\def\LTTops{\mathsf{LTTops}}
\def\Clops {\mathsf{Clops}}

\def\dnu  {{↓}u}
\def\dnou {{↓}^\circ u}
\def\dnous{(\dnou)^*}
\def\dnus {(\dnu)^*}


\def\pmt         #1{\pmat{\text{#1}}}
\def\pmtt      #1#2{\pmat{\text{#1} \\ \text{#2}}}
\def\pmttt   #1#2#3{\pmat{\text{#1} \\ \text{#2} \\ \text{#3}}}
\def\pmtttt#1#2#3#4{\pmat{\text{#1} \\ \text{#2} \\ \text{#3} \\ \text{#4}}}

\def\smt         #1{\sm{\text{#1}}}
\def\smtt      #1#2{\sm{\text{#1} \\ \text{#2}}}
\def\smttt   #1#2#3{\sm{\text{#1} \\ \text{#2} \\ \text{#3}}}
\def\smtttt#1#2#3#4{\sm{\text{#1} \\ \text{#2} \\ \text{#3} \\ \text{#4}}}




%D diagram ??
%D 2Dx     100  +50 +25 +40  +50 +25
%D 2D  100 A0 - A1      B0 - B1
%D 2D  +25 |  /     A4  |  /     B4
%D 2D  +25 A2 - A3      B2 - B3
%D 2D
%D ren A0 A1 A2 A3 A4 ==> \Pts(𝐏) \Nucs(𝐏) \GrTops(𝐏) \LTTops(𝐏) \Clops(𝐏)
%D ren B0 B1 B2 B3 B4 ==> 𝓨 \nuc J j \clop
%D
%D (( A0 A1  -> # sl^ .plabel= a \smt{C.4.2}
%D    A0 A1 <-- # sl_ .plabel= b \smt{(e-mail)}
%D    A0 A2  -> # sl_ .plabel= l \smtt{2.8,}{C.4.1}
%D    A0 A2 <-  # sl^ .plabel= r \smt{2.9}
%D    A2 A1 <-> # .plabel= m \smtt{B.8,}{B.25}
%D    A2 A3 <->
%D    A3 A4 <->
%D ))
%D (( B0 B1  <-> # sl^ .plabel= a \sm{(X↦j)}
%D  # B0 B1  |-> # sl^ .plabel= a \sm{(X↦j)}
%D  # B0 B1 <--| # sl_ .plabel= b \sm{(j↦X)}
%D    B0 B2  <-> # sl_ .plabel= l \sm{(X↦J),\\(J↦X)}
%D    B2 B1  <-> #     .plabel= m \sm{(j↦J),\\(J↦j)}
%D    B2 B3 <->
%D    B3 B4 <->
%D ))
%D enddiagram
%D
$$\pu
  \diag{??}
$$

$$\begin{array}{rrcll}
  (𝓨↦\nuc): & 𝓢^* &=&  𝓨→𝓢                              \\
  (\nuc↦𝓨): & 𝓨  &=& \setofst {u∈𝐃} {u\not∈\dnous}  \\
  [5pt]
  (𝓨↦J):  & J(u)   &=& \setofst{𝓢∈Ω(u)}{𝓨∩\dnu⊆𝓢}          \\
  (J↦𝓨):  & X_J    &=& \setofst{u∈𝐃}{J(u)=\{{↓}u\}}       \\
  [5pt]
  (\nuc↦J): & J(u) &=& \setofst {𝓢∈Ω(u)} {u∈𝓢^*}  \\
  (J↦\nuc): & 𝓢^* &=& \setofst {u∈𝐃} {𝓢∩{↓}u∈J(u)}       \\
  [5pt]
  (J↦j): & j        &=& χ_{(J \ito Ω)}     \\
  (j↦J): & J        &=& \dom(σ(j))   \\
  [5pt]
  (j↦\clop): & \ovl{(f:A \ito B)} &=& σ(j∘χ_f)  \\
  (\clop↦j): & j &=& χ_{\ovl{(1_⊤ \ito Ω)}}       \\
  [10pt]
  (\clop↦\nuc): & 𝓢^* &=& \dom(\ovl{(𝓢 \ito 1)}) \\
  [10pt]
  (\nuc↦\clop): & 𝓢^* &=& \dom(\ovl{(𝓢 \ito 1)}) \\
  \end{array}
$$

% (cltp 10 "top-to-clop")
% (clta    "top-to-clop")


$$\begin{array}{rrcll}
  (X↦j): & j_X(S) &=&  X→S                               & \text{(C.4.2, C.2)} \\
  (j↦X): & X_j    &=& \setofsc {p∈𝐏} {p\not∈j(\dnpo)}    & \text{(e-mail)} \\
  [5pt]
  (X↦J): & J_X(p) &=& \setofsc{S∈\Ddp}{X∩{↓}p⊆S}         & \text{(2.8, C.4.1)} \\
  (J↦X): & X_J    &=& \setofsc{p∈𝐏}{J(p)=\{{↓}p\}}      & \text{(2.9)} \\
  [5pt]
  (j↦J): & J_j(p) &=& \setofsc {S∈\Downs(\dnp)} {p∈j(S)} & \text{(B.8, B.25)} \\
  (J↦j): & j_J(S) &=& \setofsc {p∈𝐏} {S∩{↓}p∈J(p)}      & \text{(B.8, B.25)} \\
  \end{array}
$$




%\printbibliography

\GenericWarning{Success:}{Success!!!}  % Used by `M-x cv'

\end{document}

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

 (eepitch-shell)
 (eepitch-kill)
 (eepitch-shell)
# (find-LATEXfile "2019planar-has-1.mk")
make -f 2019.mk STEM=2021other-bijections veryclean
make -f 2019.mk STEM=2021other-bijections pdf

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