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% (find-LATEX "2022cwm.tex") % (defun c () (interactive) (find-LATEXsh "lualatex -record 2022cwm.tex" :end)) % (defun C () (interactive) (find-LATEXSH "lualatex 2022cwm.tex" "Success!!!")) % (defun D () (interactive) (find-pdf-page "~/LATEX/2022cwm.pdf")) % (defun d () (interactive) (find-pdftools-page "~/LATEX/2022cwm.pdf")) % (defun e () (interactive) (find-LATEX "2022cwm.tex")) % (defun u () (interactive) (find-latex-upload-links "2022cwm")) % (defun v () (interactive) (find-2a '(e) '(d))) % (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g)) % (defun d0 () (interactive) (find-ebuffer "2022cwm.pdf")) % (code-eec-LATEX "2022cwm") % (find-pdf-page "~/LATEX/2022cwm.pdf") % (find-sh0 "cp -v ~/LATEX/2022cwm.pdf /tmp/") % (find-sh0 "cp -v ~/LATEX/2022cwm.pdf /tmp/pen/") % file:///home/edrx/LATEX/2022cwm.pdf % file:///tmp/2022cwm.pdf % file:///tmp/pen/2022cwm.pdf % http://angg.twu.net/LATEX/2022cwm.pdf % (find-LATEX "2019.mk") % (find-lualatex-links "2022cwm" "cw2") \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") \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") %\printbibliography % (find-books "__cats/__cats.el" "maclane") % (find-cwm2page (+ 13 90) "3. Reflective Subcategories") % % B |--> C(B,-) C(B,C) g B -g-> C % ^ | | - ^ ^ % f| <-> |f^* | | f| / g∘f f^* = λg.g∘f % | v v v | / % A |--> C(A,-) C(A,C) f^*g=g∘f A % % C(B,B) id_B % | - % | | f = f^*id_B % v v % C(A,B) f^*id_B % % C(B,A) e B -e>> A all f^*s are epi % | - ^ ^ implies % v | f| / id_A f is split monic % v v ^ / % C(A,A) id_A A % % C(B,C) h∘e B -e>> A f is split monic % | - ^ ^ \ implies % v | f| id_A \ h all f^*s are epi % v v ^ / v % C(A,C) h = h∘e∘f A ---h----> C % % C(B,-) C(B,C) B -g-> C % v v ^ ^ all f^*s are monic % |f^* |f^* f^ / g∘f iff % v v | / f is epi % C(A,-) C(A,C) A % % % % % % LRB LA <--| A 1 LRB <--| RB <--| B % | | | | | | | % | | <-> | | | <-> | <-| | % v v v v v v | % B B |--> RB B |---> B(LRB,B) C |---> RC <--| C % % B <-L- A A(LRB,-) B <-L-- A <---- B % -R-> B ------> Set --R-> % % B(B,-) % \ % v % B(LRB,-) % %D diagram adjunction-1 %D 2Dx 100 +20 +20 +20 +20 %D 2D 100 A0 A2 <-| A3 A6 A9 %D 2D | | | | | %D 2D | | <-> | | | %D 2D v v v v v %D 2D +20 A1 A4 |-> A5 A7 A10 %D 2D ^ ^ %D 2D +15 AC0 AC1 <> AC2 | | %D 2D | | %D 2D +5 A8 A11 %D 2D %D 2D +15 AC3 AC4 %D 2D %D # ren ==> %D %D (( A0 A1 -> %D AC0 place %D A2 A3 <-| %D A2 A4 -> %D A3 A5 -> %D A4 A5 |-> %D A2 A5 harrownodes nil 20 nil <-> %D AC1 AC2 <- sl^ .plabel= a L %D AC1 AC2 -> sl_ .plabel= b R %D A6 A7 -> %D A7 A8 <- %D AC3 place %D A9 A10 -> %D A10 A11 <- %D AC4 place %D %D )) %D enddiagram %D $$\pu \diag{adjunction-1} $$ \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=2022cwm veryclean make -f 2019.mk STEM=2022cwm pdf % Local Variables: % coding: utf-8-unix % indent-tabs-mode: nil % ee-tla: "cw2" % End: