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% (find-sh0 "cp -v  ~/LATEX/2020lawvere-notation.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2020lawvere-notation.pdf /tmp/pen/")
%   file:///home/edrx/LATEX/2020lawvere-notation.pdf
%               file:///tmp/2020lawvere-notation.pdf
%           file:///tmp/pen/2020lawvere-notation.pdf
% http://angg.twu.net/LATEX/2020lawvere-notation.pdf
% (find-LATEX "2019.mk")

% Moved to:
% (lad)
% (ladp)

% «.defs»			(to "defs")
% «.limp-2020»			(to "limp-2020")
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\catcode`\^^J=10
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% %L dofile "edrxpict.lua"  -- (find-LATEX "edrxpict.lua")
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%                     
% «defs»  (to ".defs")

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\catcode`⊸=13 \def⊸{\limp}

% Test:
% $R {\limp}
%  S \limp
%  T \supset
%  U \bhbox{$\supset$}
%  V \bhbox{$\limp$}
%  W
% $

\setlength{\parindent}{0pt}

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%  _____ _ _   _                               
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%   |_| |_|\__|_|\___| | .__/ \__,_|\__, |\___|
%                      |_|          |___/      
%
% «title-page»  (to ".title-page")

Notes on the notation in some

very old papers by Lawvere

\newpage

\noedrxfooter



{\bf Adjointness in Foundations}

% (find-books "__cats/__cats.el" "lawvere-adjfo")
% (find-lawvereadjfopage 11 "A hyperdoctrine shall consist of")
% (find-lawvereadjfotext 11 "A hyperdoctrine shall consist of")

Adjointness in Foundations, p.11:


%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
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%D    @ 0 @ 3 harrownodes nil 20 nil <->
%D    @ 2 @ 3 <-|
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%D    @ 0 @ 3 harrownodes nil 20 nil <->
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%D ))
%D ((
%D     B0 B1 -> sl^^ .plabel= a (\,)Σf
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%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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