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Warning: this is an htmlized version!
The original is here, and the conversion rules are here. |
% (find-LATEX "2022missing-diags-yoneda.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2022missing-diags-yoneda.tex" :end))
% (defun C () (interactive) (find-LATEXSH "lualatex 2022missing-diags-yoneda.tex" "Success!!!"))
% (defun D () (interactive) (find-pdf-page "~/LATEX/2022missing-diags-yoneda.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2022missing-diags-yoneda.pdf"))
% (defun e () (interactive) (find-LATEX "2022missing-diags-yoneda.tex"))
% (defun u () (interactive) (find-latex-upload-links "2022missing-diags-yoneda"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g))
% (defun d0 () (interactive) (find-ebuffer "2022missing-diags-yoneda.pdf"))
% (code-eec-LATEX "2022missing-diags-yoneda")
% (find-pdf-page "~/LATEX/2022missing-diags-yoneda.pdf")
% (find-sh0 "cp -v ~/LATEX/2022missing-diags-yoneda.pdf /tmp/")
% (find-sh0 "cp -v ~/LATEX/2022missing-diags-yoneda.pdf /tmp/pen/")
% file:///home/edrx/LATEX/2022missing-diags-yoneda.pdf
% file:///tmp/2022missing-diags-yoneda.pdf
% file:///tmp/pen/2022missing-diags-yoneda.pdf
% http://angg.twu.net/LATEX/2022missing-diags-yoneda.pdf
% (find-LATEX "2019.mk")
% (find-lualatex-links "2022missing-diags-yoneda" "mdy")
% «.Y93+klm» (to "Y93+klm")
% «.Y3+diag» (to "Y3+diag")
% «.Y72+l» (to "Y72+l")
% «.sqcond-inner» (to "sqcond-inner")
\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{edrx21} % (find-LATEX "edrx21.sty")
\input edrxaccents.tex % (find-LATEX "edrxaccents.tex")
\input edrx21chars.tex % (find-LATEX "edrx21chars.tex")
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\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")
\def\DEMO#1{}
\def\DEMO#1{#1}
% %\def\DONTDRAWDEMOS{don't draw!} % for tests
% \ifx\DONTDRAWDEMOS\relax
% \def\DEMO#1{}
% %\else
% % \def\DEMO#1{#1}
% \fi
%
% % See: (find-dn6 "block.lua" "tf_push_and_tf_pop")
% \directlua{tf_push("2022missing-diags-yoneda.tex")}
% «Y93+klm» (to ".Y93+klm")
% (mdyp 1 "Y93+klm")
% (mdya "Y93+klm")
%D diagram Y93+klm
%D 2Dx 100 +40
%D 2D 100 A1
%D 2D |
%D 2D +25 A2 - A3
%D 2D | |
%D 2D +25 A4 - A5
%D 2D | |
%D 2D +25 A6 - A7
%D 2D | |
%D 2D +25 A8 - A9
%D 2D
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%D 2D \ |
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%D 2D
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%D ren A6 A7 ==> \ga{A6} \ga{A7}
%D ren A8 A9 ==> \ga{A8} \ga{A9}
%D ren B0 B1 ==> \ga{B0} \ga{B1}
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%D ren C3 ==> \ga{C3}
%D
%D (( A1 A3 -> .plabel= r \ga{A13}
%D A2 A3 |->
%D A2 A4 -> .plabel= l \ga{A24}
%D A3 A5 -> .plabel= r \ga{A35}
%D A2 A5 harrownodes nil 20 nil |->
%D A4 A5 |->
%D A4 A6 -> .plabel= l \ga{A46}
%D A5 A7 -> .plabel= r \ga{A57}
%D A4 A7 harrownodes nil 20 nil |->
%D A6 A7 |->
%D A6 A8 -> .plabel= l \ga{A68}
%D A7 A9 -> .plabel= r \ga{A79}
%D A6 A9 harrownodes nil 20 nil |->
%D A8 A9 |->
%D
%D A2 A6 -> .slide= -15pt .plabel= l \ga{A26}
%D A1 A5 -> .slide= 20pt .plabel= r \ga{A15}
%D A1 A7 -> .slide= 35pt .plabel= r \ga{A17}
%D
%D B0 B1 -> .plabel= a \ga{B01}
%D
%D C0 C1 -> .plabel= a \ga{C01}
%D C0 C3 -> .plabel= b \ga{C03}
%D C1 C3 <-> .plabel= r \ga{C13}
%D ))
%D enddiagram
\pu
\sa{Y00-dummynames}{
\sa{A1}{A1}
\sa{A2}{A2} \sa{A3}{A3}
\sa{A4}{A4} \sa{A5}{A5}
\sa{A6}{A6} \sa{A7}{A7}
\sa{A8}{A8} \sa{A9}{A9}
\sa{B0}{B0} \sa{B1}{B1}
\sa{C0}{C0} \sa{C1}{C1}
\sa{C3}{C3}
%
\sa{A13}{A13}
\sa{A24}{A24} \sa{A35}{A35}
\sa{A46}{A46} \sa{A57}{A57}
\sa{A68}{A68} \sa{A79}{A79}
%
\sa{A26}{A26} \sa{A15}{A15} \sa{A17}{A17}
%
\sa{B01}{B01}
\sa{C01}{C01}
\sa{C03}{C03}
\sa{C13}{C13}
%
\diag{Y93+klm}
}
\sa{Y00-basicnames}{
\sa{A1}{A}
\sa{A2}{C} \sa{A3}{RC}
\sa{A4}{D} \sa{A5}{RD}
\sa{A6}{E} \sa{A7}{RE}
\sa{A8}{F} \sa{A9}{RF}
\sa{B0}{\catB} \sa{B1}{\catA}
\sa{C0}{\catB(C,-)} \sa{C1}{\catA(A,R-)}
\sa{C3}{C3}
%
\sa{A13}{η}
\sa{A24}{f} \sa{A35}{Rf}
\sa{A46}{g} \sa{A57}{Rg}
\sa{A68}{h} \sa{A79}{Rh}
%
\sa{A26}{k} \sa{A15}{ℓ} \sa{A17}{m}
%
\sa{B01}{R}
\sa{C01}{α}
\sa{C03}{β}
\sa{C13}{♮}
%
\diag{Y93+klm}
}
\DEMO{
$$\ga{Y00-dummynames}
\qquad
\ga{Y00-basicnames}
$$
}
% «Y3+diag» (to ".Y3+diag")
% (mdyp 1 "Y3+diag")
% (mdya "Y3+diag")
%D diagram Y3+diag
%D 2Dx 100 +40
%D 2D 100 A1
%D 2D |
%D 2D +25 A2 - A3
%D 2D
%D 2D +15 B0 - B1
%D 2D
%D 2D +15 C0 - C1
%D 2D \ |
%D 2D +20 C3
%D 2D
%D ren A1 ==> \ga{A1}
%D ren A2 A3 ==> \ga{A2} \ga{A3}
%D ren B0 B1 ==> \ga{B0} \ga{B1}
%D ren C0 C1 ==> \ga{C0} \ga{C1}
%D ren C3 ==> \ga{C3}
%D
%D (( A1 A3 -> .plabel= r \ga{A13}
%D A2 A3 |->
%D
%D B0 B1 -> .plabel= a \ga{B01}
%D
%D # C0 C1 -> .plabel= a \ga{C01}
%D C0 C3 <-> .plabel= b \ga{C03}
%D # C1 C3 <-> .plabel= r \ga{C13}
%D ))
%D enddiagram
\pu
\def\Rings{\mathbf{Rings}}
\sa{Y3+diag-dummynames}{
\sa{A1}{A1}
\sa{A2}{A2} \sa{A3}{A3}
\sa{B0}{B0} \sa{B1}{B1}
\sa{C0}{C0} %\sa{C1}{C1}
\sa{C3}{C3}
%
\sa{A13}{A13}
%
\sa{B01}{B01}
%\sa{C01}{C01}
\sa{C03}{C03}
%\sa{C13}{C13}
%
\diag{Y3+diag}
}
\sa{Y3+diag-Z[x]}{
\sa{A1}{1}
\sa{A2}{\Z[x]} \sa{A3}{U(\Z[x])}
\sa{B0}{\Rings} \sa{B1}{\Set}
\sa{C0}{\Rings(\Z[x],-)} %\sa{C1}{C1}
\sa{C3}{U}
%
\sa{A13}{\nameof{x}}
\sa{B01}{U}
%\sa{C01}{C01}
\sa{C03}{}
%\sa{C13}{C13}
%
\diag{Y3+diag}
}
\DEMO{
$$\ga{Y3+diag-dummynames}
\qquad
\ga{Y3+diag-Z[x]}
$$
}
\newpage
% «Y72+l» (to ".Y72+l")
% (mdyp 3 "Y72+l")
% (mdya "Y72+l")
%D diagram Y72+l
%D 2Dx 100 +40
%D 2D 100 A1
%D 2D |
%D 2D +25 A2 - A3
%D 2D | |
%D 2D +25 A4 - A5
%D 2D | |
%D 2D +25 A6 - A7
%D 2D
%D 2D +15 B0 - B1
%D 2D
%D 2D +15 C0 - C1
%D 2D
%D ren A1 ==> \ga{A1}
%D ren A2 A3 ==> \ga{A2} \ga{A3}
%D ren A4 A5 ==> \ga{A4} \ga{A5}
%D ren A6 A7 ==> \ga{A6} \ga{A7}
%D ren B0 B1 ==> \ga{B0} \ga{B1}
%D ren C0 C1 ==> \ga{C0} \ga{C1}
%D
%D (( A1 A3 -> .plabel= r \ga{A13}
%D A2 A3 |->
%D A2 A4 -> .plabel= l \ga{A24}
%D A3 A5 -> .plabel= r \ga{A35}
%D A2 A5 harrownodes nil 20 nil |->
%D A4 A5 |->
%D A4 A6 -> .plabel= l \ga{A46}
%D A5 A7 -> .plabel= r \ga{A57}
%D A4 A7 harrownodes nil 20 nil |->
%D A6 A7 |->
%D
%D # A2 A6 -> .slide= -15pt .plabel= l \ga{A26}
%D A1 A5 -> .slide= 20pt .plabel= r \ga{A15}
%D # A1 A7 -> .slide= 35pt .plabel= r \ga{A17}
%D
%D B0 B1 -> .plabel= a \ga{B01}
%D
%D C0 C1 -> .plabel= a \ga{C01}
%D ))
%D enddiagram
\pu
\sa{Y72+l-dummynames}{{
\sa{A1}{A1}
\sa{A2}{A2} \sa{A3}{A3}
\sa{A4}{A4} \sa{A5}{A5}
\sa{A6}{A6} \sa{A7}{A7}
\sa{A8}{A8} \sa{A9}{A9}
\sa{B0}{B0} \sa{B1}{B1}
\sa{C0}{C0} \sa{C1}{C1}
\sa{C3}{C3}
%
\sa{A13}{A13}
\sa{A24}{A24} \sa{A35}{A35}
\sa{A46}{A46} \sa{A57}{A57}
\sa{A68}{A68} \sa{A79}{A79}
%
\sa{A26}{A26} \sa{A15}{A15} \sa{A17}{A17}
%
\sa{B01}{B01}
\sa{C01}{C01}
\sa{C03}{C03}
\sa{C13}{C13}
%
\diag{Y72+l}
}}
\sa{Y72+l-basicnames}{{
\sa{A1}{A}
\sa{A2}{C} \sa{A3}{RC}
\sa{A4}{D} \sa{A5}{RD}
\sa{A6}{E} \sa{A7}{RE}
\sa{B0}{\catB} \sa{B1}{\catA}
\sa{C0}{\catB(C,-)} \sa{C1}{\catA(A,R-)}
\sa{A13}{η}
\sa{A24}{f} \sa{A35}{Rf}
\sa{A46}{g} \sa{A57}{Rg}
%
\sa{A15}{ℓ}
%
\sa{B01}{R}
\sa{C01}{α}
%
\diag{Y72+l}
}}
\sa{Y72+l-idC}{{
\sa{A1}{A}
\sa{A2}{C} \sa{A3}{RC}
\sa{A4}{C} \sa{A5}{RC}
\sa{A6}{D} \sa{A7}{RD}
\sa{B0}{\catB} \sa{B1}{\catA}
\sa{C0}{\catB(C,-)} \sa{C1}{\catA(A,R-)}
\sa{A13}{η}
\sa{A24}{ι} \sa{A35}{Rι}
\sa{A46}{f} \sa{A57}{Rf}
%
\sa{A15}{\sm{m,\\αCι}}
%
\sa{B01}{R}
\sa{C01}{α}
%
\diag{Y72+l}
}}
$$%\ga{Y72+l-dummynames}
%\qquad
\scalebox{0.8}{$
\ga{Y72+l-basicnames}
\qquad
\ga{Y72+l-idC}
$}
$$
\def\HomA#1{HomA(#1)}
\def\HomB#1{HomB(#1)}
\def\HomA#1{\catA(#1)}
\def\HomB#1{\catB(#1)}
% «sqcond-inner» (to ".sqcond-inner")
% (mdyp 3 "sqcond-inner")
% (mdya "sqcond-inner")
%D diagram sqcond-inner
%D 2Dx 100 +30 +40 +35 +40 +40
%D 2D 100 A0 B0 -> B1 D0 -> D1 E1
%D 2D | | | | | |
%D 2D +17 v v v v D3' E3'
%D 2D +8 A1 B2 -> B3 D2 -> D3
%D 2D
%D 2D +15 C0 -> C1
%D 2D
%D ren A0 B0 B1 D0 D1 ==> \ga{A0} \ga{B0} \ga{B1} \ga{D0} \ga{D1}
%D ren A1 B2 B3 D2 D3 ==> \ga{A1} \ga{B2} \ga{B3} \ga{D2} \ga{D3}
%D ren D3' E1 E3' C0 C1 ==> \ga{D3'} \ga{E1} \ga{E3'} \ga{C0} \ga{C1}
%D
%D (( A0 A1 -> .plabel= l \ga{A01}
%D B0 B1 -> .plabel= a \ga{B01}
%D B0 B2 -> .plabel= l \ga{B02}
%D B1 B3 -> .plabel= r \ga{B13}
%D B2 B3 -> .plabel= a \ga{B23}
%D C0 C1 -> .plabel= a \ga{C01}
%D D0 D1 |->
%D D1 D3' |->
%D D0 D2 |->
%D D2 D3 |->
%D E1 E3' |->
%D ))
%D enddiagram
%D
\pu
\sa{sqcond-nonames}{{
\sa{A0}{A0} \sa{B0}{B0} \sa{B1}{B1} \sa{D0}{D0} \sa{D1}{D1} \sa{D1}{D1}
\sa{D3'}{D3'} \sa{E3'}{E3'}
\sa{A1}{A1} \sa{B2}{B2} \sa{B3}{B3} \sa{D2}{D2} \sa{D3}{D3}
\sa{C0}{C0} \sa{C1}{C1}
\sa{A01}{A01}
\sa{B01}{B01}
\sa{B02}{B02}
\sa{B13}{B13}
\sa{B23}{B23}
\sa{C01}{C01}
\diag{sqcond-inner}
}}
\sa{sqcond-alpha}{{
\sa{A0}{D} \sa{B0}{\catB(C,D)} \sa{B1}{\catA(A,RD)}
\sa{A1}{E} \sa{B2}{\catB(C,E)} \sa{B3}{\catA(A,RE)}
\sa{C0}{\catB(C,-)} \sa{C1}{\catA(A,R-)}
\sa{D0}{f} \sa{D1}{αDf} \sa{E1}{ℓ}
\sa{D3'}{Rg∘(αDf)} \sa{E3'}{Rg∘ℓ}
\sa{D2}{g∘f} \sa{D3}{αE(g∘f)}
\sa{A01}{g}
\sa{B01}{}
\sa{B02}{}
\sa{B13}{}
\sa{B23}{}
\sa{C01}{α}
\diag{sqcond-inner}
}}
\sa{sqcond-eta}{{
\sa{A0}{D} \sa{B0}{\catB(C,D)} \sa{B1}{\catA(A,RD)}
\sa{A1}{E} \sa{B2}{\catB(C,E)} \sa{B3}{\catA(A,RE)}
\sa{C0}{\catB(C,-)} \sa{C1}{\catA(A,R-)}
\sa{D0}{f} \sa{D1}{Rf∘η} \sa{E1}{ℓ}
\sa{D3'}{Rg∘(Rf∘η)} \sa{E3'}{Rg∘ℓ}
\sa{D2}{g∘f} \sa{D3}{R(g∘f)∘η}
\sa{A01}{g}
\sa{B01}{}
\sa{B02}{}
\sa{B13}{}
\sa{B23}{}
\sa{C01}{α_η}
\diag{sqcond-inner}
}}
\sa{sqcond-idC-iota}{{
\sa{A0}{C} \sa{B0}{\catB(C,C)} \sa{B1}{\catA(A,RC)}
\sa{A1}{D} \sa{B2}{\catB(C,D)} \sa{B3}{\catA(A,RD)}
\sa{C0}{\catB(C,-)} \sa{C1}{\catA(A,R-)}
\sa{D0}{ι} \sa{D1}{αCι} \sa{E1}{m}
\sa{D3'}{Rg∘(αCι)} \sa{E3'}{Rf∘m}
\sa{D2}{f∘ι} \sa{D3}{αD(f∘ι)}
\sa{A01}{f}
\sa{B01}{}
\sa{B02}{}
\sa{B13}{}
\sa{B23}{}
\sa{C01}{α}
\diag{sqcond-inner}
}}
%$$\ga{sqcond-nonames}
%$$
$$\ga{sqcond-alpha}
$$
$$\ga{sqcond-eta}
$$
$$\ga{sqcond-idC-iota}
$$
% \directlua{tf_pop()}
\GenericWarning{Success:}{Success!!!} % Used by `M-x cv'
\end{document}
% Local Variables:
% coding: utf-8-unix
% ee-tla: "mdy"
% End: