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

% «.3.»	(to "3.")
% «.5.»	(to "5.")
% «.8.»	(to "8.")

\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")

% (find-books "__cats/__cats.el" "badiou")


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

Notes on Alain Badiou's

``Mathematics of The Transcendental - Onto-Logy and Being-There'' (2014):

\url{https://www.bloomsbury.com/us/mathematics-of-the-transcendental-9781441189240/}

\ssk

These notes are at:

\url{http://angg.twu.net/LATEX/2020badiou-mt.pdf}

}


% «3.»  (to ".3.")
% (find-books "__cats/__cats.el" "badiou")
% (find-badioumtpage (+ 9 21) "3 The Size of a Category")
% (find-badioumttext (+ 9 21) "3 The Size of a Category")
% (find-badioumtpage (+ 9 25) "cone")
% (find-badioumttext (+ 9 25) "cone")

\section*{3. The size of a category}

(Page 25: cone)

%D diagram cone
%D 2Dx     100 +15 +15 +30 +20 +30 +25
%D 2D  100     A0      B0  B1  C0  C1
%D 2D
%D 2D  +20 A1 ---> A2  B2  B3  C2
%D 2D
%D ren A0 A1 A2    ==> c a_1 a_2
%D ren B0 B1 B2 B3 ==> c c a_1 a_2
%D ren C0 C1 C2    ==> (c\ton{\id}c) c (a_1\ton{f}a_2)
%D
%D (( A0 A1 -> .plabel= l g_1
%D    A0 A2 -> .plabel= r g_2 
%D    A1 A2 -> .plabel= b f
%D    A1 A2 midpoint xy+= 0 15 .TeX= f∘g_1=g_2 place
%D    B0 B1 -> .plabel= a \id
%D    B0 B2 -> .plabel= l g_1
%D    B1 B3 -> .plabel= r g_2
%D    B2 B3 -> .plabel= a f
%D    C0 C1 <-|
%D    C0 C2 -> .plabel= l (g_1,g_2)
%D ))
%D enddiagram
%D
$$\pu
  \diag{cone}
$$



% «5.»  (to ".5.")
% (find-badioumtpage (+ 9 29) "5 SOME FUNDAMENTAL" "CONCEPTS")
% (find-badioumttext (+ 9 29) "5 SOME FUNDAMENTAL" "CONCEPTS")

\section*{5. Some fundamental concepts}

(Page 30): Limit of the diagram with two objects without arrows:

%D diagram ??
%D 2Dx     100 +20 +20 +30 +20 +20 +50 +25 +20
%D 2D  100     A0          B0      C0  C1
%D 2D
%D 2D  +20 A1  A2  A3  B1  B2  B3  C2  C3
%D 2D
%D 2D  +20                         C4
%D 2D
%D ren A0 A1 A2 A3 ==> c' a c b
%D ren B0 B1 B2 B3 ==> ∀c' a c b
%D ren C0 C1 C2 C3 C4 ==> (c'\;\;c') c' (c\;\;c) c (a\;\;b)
%D
%D (( A0 A1 -> .plabel= a g_1
%D    A0 A2 -> .plabel= r h
%D    A0 A3 -> .plabel= a g_2
%D    A1 A2 <- .plabel= b f_1
%D    A2 A3 -> .plabel= b f_2
%D    B0 B1 -> .plabel= a ∀g_1
%D    B0 B2 -> .plabel= m ∃!h  
%D    B0 B3 -> .plabel= a ∀g_2
%D    B1 B2 <- .plabel= b f_1
%D    B2 B3 -> .plabel= b f_2
%D    C0 C1 <-|
%D    C0 C2 -> .plabel= l (h,h)
%D    C1 C3 -> .plabel= r ∃!h
%D    C2 C3 <-|
%D    C2 C4 -> .plabel= l (f_1,f_2)
%D    C0 C4 -> .slide= -30pt .plabel= l ∀(g_1,g_2)
%D    C0 C3 harrownodes nil 20 nil <-|
%D ))
%D enddiagram
%D
$$\pu
  \diag{??}
$$

(Page 33): Pullback


%D diagram ??
%D 2Dx     100 +20 +20 +60 +35
%D 2D  100 A0          B0  B1
%D 2D
%D 2D  +20     A1  A2  B2  B3
%D 2D
%D 2D  +20     A3  A4  B4
%D 2D
%D ren A0 A1 A2 A3 A4 ==> c' c a_1 a_2 b
%D ren B0 B1 ==> (c'{\ton{\id}}c'{\otn{\id}}c') c'
%D ren B2 B3 ==>  (c{\ton{\id}}c{\otn{\id}}c)   c
%D ren B4    ==>  (a_1{\ton{f}}b{\otn{g}}a_2)
%D
%D (( A0 A1 -> .plabel= m ∃!k
%D    A0 A2 -> .plabel= a ∀i_1
%D    A0 A3 -> .plabel= l ∀i_2
%D    A1 A2 -> .plabel= b h_1 
%D    A1 A3 -> .plabel= r h_2
%D    A2 A4 -> .plabel= r f
%D    A3 A4 -> .plabel= b g
%D    
%D    B0 B1 <-|
%D    B0 B2 -> .plabel= l (h,\_,h)
%D    B1 B3 -> .plabel= r ∃!h
%D    B2 B3 <-|
%D    B2 B4 -> .plabel= l (f_1,\_,f_2)
%D    B0 B4 -> .slide= -40pt .plabel= l ∀(i_1,\_,i_2)
%D    B0 B3 harrownodes nil 20 nil <-|
%D ))
%D enddiagram
%D
$$\pu
  \diag{??}
$$

\newpage

% «8.»  (to ".8.")
% (find-badioumtpage (+ 9 45) "8 EXPONENTIATION")
% (find-badioumttext (+ 9 45) "8 EXPONENTIATION")


\section*{8. Exponentiation}

(Page 48):

\def\pr{\mathrm{pr}}

%D diagram ??
%D 2Dx     100 +25 +25 +20 +25 +25 +20
%D 2D  100 A0  A1  A2      B0
%D 2D
%D 2D  +20 A3  A4  A5  B1  B2  B3
%D 2D
%D ren A0 A1 A2    ==> a a×c c
%D ren A3 A4 A5    ==> b b×d d
%D ren B0 B1 B2 B3 ==> a×c b b×d d
%D
%D (( A0 A1 <- .plabel= a \pr_a
%D    A1 A2 -> .plabel= a \pr_c
%D    A0 A3 -> .plabel= l f
%D    A2 A5 -> .plabel= r g
%D    A3 A4 <- .plabel= a \pr_b
%D    A4 A5 -> .plabel= a \pr_c
%D    B0 B1 -> .plabel= a f∘\pr_a
%D    B0 B2 -> .plabel= m f×g
%D    B0 B3 -> .plabel= a g∘\pr_c
%D    B1 B2 <- .plabel= b \pr_b
%D    B2 B3 -> .plabel= b \pr_d
%D ))
%D enddiagram
%D
$$\pu
  \diag{??}
  \qquad
  \mat{f×g:= \\ 〈f∘\pr_a,\;g∘\pr_c〉}
$$

(Page 49):


%D diagram exp-p49-1
%D 2Dx     100 +10 +25 +20 +20 +20 +20
%D 2D  100 A0  B0  C0
%D 2D
%D 2D  +15             C1
%D 2D
%D 2D  +15 A1  B1  C2
%D 2D
%D ren A0 A1 ==> B^A C
%D ren B0 B1 ==> A A
%D ren C0 C1 C2 ==> B^A×A B C×A
%D
%D (( A0 A1 <- .plabel= l \hat{g}
%D    B0 B1 <- .plabel= r \id
%D    C0 C2 <- .plabel= l \hat{g}×\id
%D    C0 C1 -> .plabel= r \ev
%D    C2 C1 -> .plabel= r g
%D ))
%D enddiagram
%D
%D diagram exp-p49-2
%D 2Dx     100 +30
%D 2D  100 A0  A1
%D 2D
%D 2D  +20 A2  A3
%D 2D
%D 2D  +20 A4
%D 2D
%D ren A0 A1 ==> C×A ∀C
%D ren A2 A3 ==> B^A×A B^A
%D ren A4    ==> B
%D
%D ((
%D    A0 A1 <-|
%D    A0 A2 -> .plabel= l \sm{(×A)\hat{g}\;=\\\hat{g}×\id}
%D    A1 A3 -> .plabel= r ∃!\hat{g}
%D    A2 A3 <-|
%D    A2 A4 -> .plabel= l \ev
%D    A0 A4 -> .slide= -40pt .plabel= l ∀g
%D    A0 A3 harrownodes nil 20 nil <-|
%D
%D ))
%D enddiagram
%D
$$\pu
  \diag{exp-p49-1}
  \qquad
  \diag{exp-p49-2}
$$





\end{document}

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# (find-LATEXfile "2019planar-has-1.mk")
make -f 2019.mk STEM=2020badiou-mt veryclean
make -f 2019.mk STEM=2020badiou-mt pdf

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