|
Warning: this is an htmlized version!
The original is here, and the conversion rules are here. |
% (find-LATEX "2020seelyhyp-poster.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2020seelyhyp-poster.tex" :end))
% (defun d () (interactive) (find-pdf-page "~/LATEX/2020seelyhyp-poster.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2020seelyhyp-poster.pdf"))
% (defun e () (interactive) (find-LATEX "2020seelyhyp-poster.tex"))
% (defun u () (interactive) (find-latex-upload-links "2020seelyhyp-poster"))
% (defun v () (interactive) (find-2a '(e) '(d)) (g))
% (find-pdf-page "~/LATEX/2020seelyhyp-poster.pdf")
% (find-sh0 "cp -v ~/LATEX/2020seelyhyp-poster.pdf /tmp/")
% (find-sh0 "cp -v ~/LATEX/2020seelyhyp-poster.pdf /tmp/pen/")
% file:///home/edrx/LATEX/2020seelyhyp-poster.pdf
% file:///tmp/2020seelyhyp-poster.pdf
% file:///tmp/pen/2020seelyhyp-poster.pdf
% http://angg.twu.net/LATEX/2020seelyhyp-poster.pdf
% (find-LATEX "2019.mk")
% «.adjoints-generic» (to "adjoints-generic")
% «.adjoints-quants» (to "adjoints-quants")
% «.adjoints-equal» (to "adjoints-equal")
% «.adjoints-f» (to "adjoints-f")
\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")
%
%\usepackage[backend=biber,
% style=alphabetic]{biblatex} % (find-es "tex" "biber")
%\addbibresource{catsem-slides.bib} % (find-LATEX "catsem-slides.bib")
%
% (find-es "tex" "limp-abx")
\DeclareFontFamily{U}{matha}{\hyphenchar\font45}
\DeclareFontShape{U}{matha}{m}{n}{
<5> <6> <7> <8> <9> <10> gen * matha
<10.95> matha10 <12> <14.4> <17.28> <20.74> <24.88> matha12
}{}
\DeclareSymbolFont{matha}{U}{matha}{m}{n}
\DeclareMathSymbol{\varsubset}{3}{matha}{"80}
\DeclareMathSymbol{\varsupset}{3}{matha}{"81}
\def\limp{\varsupset}
\catcode`⊸=13 \def⊸{\limp}
%
% (find-es "tex" "geometry")
\begin{document}
\catcode`\^^J=10
\directlua{dofile "dednat6load.lua"} % (find-LATEX "dednat6load.lua")
\def\pded#1{\left(\cded{#1}\right)}
\def\pdedscale#1#2{\scalebox{#1}{$\pded{#2}$}}
\def\eo #1#2{#1{=}#2}
\def\ea#1#2#3{#1{=}#2∧#3}
\def\ei#1#2#3{#1{=}#2⊸#3}
% _ _ _ __ _
% / \ __| |(_) / _| __ _ ___ _ __ ___ _ __(_) ___
% / _ \ / _` || | | |_ / _` |/ _ \ '_ \ / _ \ '__| |/ __|
% / ___ \ (_| || | | _| | (_| | __/ | | | __/ | | | (__
% /_/ \_\__,_|/ | |_| \__, |\___|_| |_|\___|_| |_|\___|
% |__/ |___/
%
% «adjoints-generic» (to ".adjoints-generic")
Adjoints to an arbitrary $f^*$:
\bsk
%D diagram adjs-generic
%D 2Dx 100 +40
%D 2D 100 A0 |-> A1
%D 2D | |
%D 2D | |-> |
%D 2D | |
%D 2D +25 A2 |-> A3
%D 2D | |
%D 2D | <-> |
%D 2D | |
%D 2D +25 B0 <-| B1
%D 2D | |
%D 2D | <-| |
%D 2D | |
%D 2D +25 B2 <-| B3
%D 2D | |
%D 2D | <-> |
%D 2D | |
%D 2D +25 C0 |-> C1
%D 2D | |
%D 2D | |-> |
%D 2D | |
%D 2D +25 C2 |-> C3
%D 2D
%D 2D +20 D0 <=> D1
%D 2D
%D 2D +20 E2 --> E3
%D 2D
%D ren A0 A1 ==> A_1 Σ_fA_1
%D ren A2 A3 ==> A_2 Σ_fA_2
%D ren B0 B1 ==> f^*B_1 B_1
%D ren B2 B3 ==> f^*B_2 B_2
%D ren C0 C1 ==> C_1 Π_fC_1
%D ren C2 C3 ==> C_2 Π_fC_2
%D ren D0 D1 ==> 𝐛P(X) 𝐛P(Y)
%D ren E2 E3 ==> X Y
%D
%D (( A0 A1 |->
%D A2 A3 |->
%D B0 B1 <-|
%D B2 B3 <-|
%D C0 C1 |->
%D C2 C3 |->
%D A0 A3 harrownodes nil 20 nil |->
%D A2 B1 harrownodes nil 20 nil |-> sl^
%D A2 B1 harrownodes nil 20 nil <-| sl_
%D B0 B3 harrownodes nil 20 nil <-|
%D B2 C1 harrownodes nil 20 nil <-| sl^
%D B2 C1 harrownodes nil 20 nil |-> sl_
%D C0 C3 harrownodes nil 20 nil |->
%D A0 A2 -> .plabel= l α
%D A1 A3 -> .plabel= r Σ_fα
%D A2 B0 -> .plabel= l \sm{f\\(Σ_f^♯)g}
%D A3 B1 -> .plabel= r \sm{(Σ_f^♭)f\\g}
%D B0 B2 -> .plabel= l f^*β
%D B1 B3 -> .plabel= r β
%D B2 C0 -> .plabel= l \sm{(Π_f^♭)h\\k}
%D B3 C1 -> .plabel= r \sm{h\\(Π_f^♯)k}
%D C0 C2 -> .plabel= l γ
%D C1 C3 -> .plabel= r Π_fγ
%D D0 D1 -> sl^^ .plabel= a Σ_f
%D D0 D1 <- .plabel= m f^*
%D D0 D1 -> sl__ .plabel= b Π_f
%D E2 E3 -> .plabel= a f
%D ))
%D enddiagram
%D
$$\pu
\diag{adjs-generic}
$$
\newpage
% _ _ _ _
% / \ __| |(_) __ _ _ _ __ _ _ __ | |_ ___
% / _ \ / _` || | / _` | | | |/ _` | '_ \| __/ __|
% / ___ \ (_| || | | (_| | |_| | (_| | | | | |_\__ \
% /_/ \_\__,_|/ | \__, |\__,_|\__,_|_| |_|\__|___/
% |__/ |_|
%
% «adjoints-quants» (to ".adjoints-quants")
Quantifiers as adjoints to adding a variable:
\bsk
%:
%: [\Pxy]^1
%: ::::::α
%: \Qxy
%: --------
%: \Exy\Pxy \Exy\Qxy
%: ----------------------1
%: \Exy\Qxy
%:
%: ^Sigmapi-F
%:
%:
%: \Qxy
%: --------
%: \Exy\Qxy
%: :::
%: \Rx
%:
%: ^Sigmapi-transposeleft
%:
%: [\Qxy]^1
%: :::f
%: \Exy\Qxy \Rx
%: ---------------1
%: \Rx
%:
%: ^Sigmapi-transposeright
%:
%:
%: \Rx
%: :::β
%: \Sx
%:
%: ^pistar-F
%:
%:
%: \Sx
%: ::::::::k
%: \Fay\Txy
%: --------
%: \Txy
%:
%: ^Pipi-transposeleft
%:
%: [\Sx]^1
%: ::::
%: \Sx \Txy
%: ---------
%: \Fay\Txy
%:
%: ^Pipi-transposeright
%:
%:
%:
%: \Fay\Txy [\Txy]^1
%: -------- ::::γ
%: \Txy \Uxy
%: ----------------
%: \Fay\Uxy
%:
%: ^Pipi-F
%:
\def\Pxy{Pxy}
\def\Qxy{Qxy}
\def\Rx {Rx}
\def\Sx {Sx}
\def\Txy{Txy}
\def\Uxy{Uxy}
\def\Exy{∃y.}
\def\Fay{∀y.}
%D diagram adjs-pi*
%D 2Dx 100 +40
%D 2D 100 A0 |-> A1
%D 2D | |
%D 2D | |-> |
%D 2D | |
%D 2D +25 A2 |-> A3
%D 2D | |
%D 2D | <-> |
%D 2D | |
%D 2D +25 B0 <-| B1
%D 2D | |
%D 2D | <-| |
%D 2D | |
%D 2D +25 B2 <-| B3
%D 2D | |
%D 2D | <-> |
%D 2D | |
%D 2D +25 C0 |-> C1
%D 2D | |
%D 2D | |-> |
%D 2D | |
%D 2D +25 C2 |-> C3
%D 2D
%D 2D +20 D0 <=> D1
%D 2D
%D 2D +20 E0 |-> E1
%D 2D +10 E2 --> E3
%D 2D
%D ren A0 A1 ==> \Pxy \Exy\Pxy
%D ren A2 A3 ==> \Qxy \Exy\Qxy
%D ren B0 B1 ==> \Rx \Rx
%D ren B2 B3 ==> \Sx \Sx
%D ren C0 C1 ==> \Txy \Fay\Txy
%D ren C2 C3 ==> \Uxy \Fay\Uxy
%D ren D0 D1 ==> 𝐛P(X{×}Y) 𝐛P(X)
%D ren E0 E1 ==> (x,y) x
%D ren E2 E3 ==> X{×}Y X
%D
%D (( A0 A1 |->
%D A2 A3 |->
%D B0 B1 <-|
%D B2 B3 <-|
%D C0 C1 |->
%D C2 C3 |->
%D A0 A3 harrownodes nil 20 nil |->
%D A2 B1 harrownodes nil 20 nil |-> sl^
%D A2 B1 harrownodes nil 20 nil <-| sl_
%D B0 B3 harrownodes nil 20 nil <-|
%D B2 C1 harrownodes nil 20 nil <-| sl^
%D B2 C1 harrownodes nil 20 nil |-> sl_
%D C0 C3 harrownodes nil 20 nil |->
%D A0 A2 -> .plabel= l α
%D A1 A3 -> .plabel= r Σ_πα
%D A2 B0 -> .plabel= l \sm{f\\(Σ_π^♯)g}
%D A3 B1 -> .plabel= r \sm{(Σ_π^♭)f\\g}
%D B0 B2 -> .plabel= l π^*β
%D B1 B3 -> .plabel= r β
%D B2 C0 -> .plabel= l \sm{(Π_π^♭)h\\k}
%D B3 C1 -> .plabel= r \sm{h\\(Π_π^♯)k}
%D C0 C2 -> .plabel= l γ
%D C1 C3 -> .plabel= r Π_πγ
%D D0 D1 -> sl^^ .plabel= a Σ_π
%D D0 D1 <- .plabel= m π^*
%D D0 D1 -> sl__ .plabel= b Π_π
%D E0 E1 |->
%D E2 E3 -> .plabel= a π
%D
%D A1 A3 midpoint relplace 55 0 Σ_πα:=\pdedscale{0.55}{Sigmapi-F}
%D A3 B1 midpoint relplace 55 0 (Σ_π^♭)f:=\pdedscale{0.55}{Sigmapi-transposeright}
%D A2 B0 midpoint relplace -50 0 (Σ_π^♯)g:=\pdedscale{0.45}{Sigmapi-transposeleft}
%D B0 B2 midpoint relplace -50 0 π^*β:=\pdedscale{0.55}{pistar-F}
%D B2 C0 midpoint relplace -50 0 (Π_π^♭)h:=\pdedscale{0.40}{Pipi-transposeleft}
%D B3 C1 midpoint relplace 50 0 (Π_π^♯)k:=\pdedscale{0.40}{Pipi-transposeright}
%D C1 C3 midpoint relplace 55 0 Π_πγ:=\pdedscale{0.55}{Pipi-F}
%D ))
%D enddiagram
%D
\pu
\phantom{a}
\hspace{-20pt}
$
\diag{adjs-pi*}
$
\newpage
% _ _ _
% / \ __| |(_) _____
% / _ \ / _` || | |_____|
% / ___ \ (_| || | |_____|
% /_/ \_\__,_|/ |
% |__/
%
% «adjoints-equal» (to ".adjoints-equal")
Equality as an adjoint to collapsing two variables:
\bsk
\def\exx {x{=}x}
\def\exxp{x{=}x'}
\def\Px {Px}
\def\Qx {Qx}
\def\Rxx {Rxx}
\def\Rxxp{Rxx'}
\def\Sxx {Sxx}
\def\Sxxp{Sxx'}
\def\Tx {Tx}
\def\Ux {Ux}
%:
%: \exxp∧\Px
%: ---------
%: \exxp∧\Px \Px
%: --------- :::α
%: \exxp \Qx
%: ----------------
%: \exxp∧\Qx
%:
%: ^SigmaD-F
%:
%:
%: ----
%: \exx \Qx [\exxp∧\Qx]^1
%: ---------- :::::::::::g
%: \exx∧\Qx \Rxxp
%: --------------------[x':=x];1
%: \Rxx
%:
%: ^SigmaD-transposeleft
%:
%: \exxp∧\Qx
%: ---------
%: \exxp∧\Qx \Qx
%: --------- ::::f
%: \exxp \Rxx
%: -----------------
%: \Rxxp
%:
%: ^SigmaD-transposeright
%:
%:
%:
%:
%: [\Rxxp]^1
%: :::::::::β
%: \Rxx \Sxxp
%: ------------[x':=x];1
%: \Sxx
%:
%: ^Dstar-F
%:
%:
%:
%:
%: [\Sxxp]^1
%: :::::::::h
%: \Sxx \exxp⊸\Tx
%: ---- ----------------[x':=x];1
%: \exx \exx⊸\Tx
%: ----------------
%: \Tx
%:
%: ^PiD-transposeleft
%:
%: [\Sxx]^1
%: ::::::::k
%: \Tx
%: --------1
%: [\exxp]^2 \Sxx⊸\Tx
%: --------------------
%: \Sxxp \Sxxp⊸\Tx
%: ------------------
%: \Tx
%: ---------2
%: \exxp⊸\Tx
%:
%: ^PiD-transposeright
%:
%: [\exxp]^1 \exxp⊸\Tx
%: ---------------------
%: \Tx
%: :::γ
%: \Ux
%: ---------1
%: \exxp⊸\Ux
%:
%: ^PiD-F
%:
%D diagram adjs-Delta*
%D 2Dx 100 +40
%D 2D 100 A0 |-> A1
%D 2D | |
%D 2D | |-> |
%D 2D | |
%D 2D +25 A2 |-> A3
%D 2D | |
%D 2D | <-> |
%D 2D | |
%D 2D +25 B0 <-| B1
%D 2D | |
%D 2D | <-| |
%D 2D | |
%D 2D +25 B2 <-| B3
%D 2D | |
%D 2D | <-> |
%D 2D | |
%D 2D +25 C0 |-> C1
%D 2D | |
%D 2D | |-> |
%D 2D | |
%D 2D +25 C2 |-> C3
%D 2D
%D 2D +20 D0 <=> D1
%D 2D
%D 2D +20 E0 |-> E1
%D 2D +10 E2 --> E3
%D 2D
%D ren A0 A1 ==> \Px \exxp∧\Px
%D ren A2 A3 ==> \Qx \exxp∧\Qx
%D ren B0 B1 ==> \Rxx \Rxxp
%D ren B2 B3 ==> \Sxx \Sxxp
%D ren C0 C1 ==> \Tx \exxp⊸\Tx
%D ren C2 C3 ==> \Ux \exxp⊸\Ux
%D ren D0 D1 ==> 𝐛P(X) 𝐛P(X{×}X)
%D ren E0 E1 ==> x (x,x')
%D ren E2 E3 ==> X X{×}X
%D
%D (( A0 A1 |->
%D A2 A3 |->
%D B0 B1 <-|
%D B2 B3 <-|
%D C0 C1 |->
%D C2 C3 |->
%D A0 A3 harrownodes nil 20 nil |->
%D A2 B1 harrownodes nil 20 nil |-> sl^
%D A2 B1 harrownodes nil 20 nil <-| sl_
%D B0 B3 harrownodes nil 20 nil <-|
%D B2 C1 harrownodes nil 20 nil <-| sl^
%D B2 C1 harrownodes nil 20 nil |-> sl_
%D C0 C3 harrownodes nil 20 nil |->
%D A0 A2 -> .plabel= l α
%D A1 A3 -> .plabel= r Σ_Δα
%D A2 B0 -> .plabel= l \sm{f\\(Σ_Δ^♯)g}
%D A3 B1 -> .plabel= r \sm{(Σ_Δ^♭)f\\g}
%D B0 B2 -> .plabel= l Δ^*β
%D B1 B3 -> .plabel= r β
%D B2 C0 -> .plabel= l \sm{(Π_Δ^♭)h\\k}
%D B3 C1 -> .plabel= r \sm{h\\(Π_Δ^♯)k}
%D C0 C2 -> .plabel= l γ
%D C1 C3 -> .plabel= r Π_Δγ
%D D0 D1 -> sl^^ .plabel= a Σ_Δ
%D D0 D1 <- .plabel= m Δ^*
%D D0 D1 -> sl__ .plabel= b Π_Δ
%D E0 E1 |->
%D E2 E3 -> .plabel= a Δ
%D
%D A1 A3 midpoint relplace 65 0 Σ_Δα:=\pdedscale{0.55}{SigmaD-F}
%D A3 B1 midpoint relplace 65 0 (Σ_Δ^♭)f:=\pdedscale{0.55}{SigmaD-transposeright}
%D A2 B0 midpoint relplace -65 0 (Σ_Δ^♯)g:=\pdedscale{0.45}{SigmaD-transposeleft}
%D B0 B2 midpoint relplace -65 0 Δ^*β:=\pdedscale{0.55}{Dstar-F}
%D B2 C0 midpoint relplace -65 0 (Π_Δ^♭)h:=\pdedscale{0.40}{PiD-transposeleft}
%D B3 C1 midpoint relplace 65 0 (Π_Δ^♯)k:=\pdedscale{0.40}{PiD-transposeright}
%D C1 C3 midpoint relplace 65 0 Π_Δγ:=\pdedscale{0.55}{PiD-F}
%D ))
%D enddiagram
%D
\pu
\phantom{a}
\hspace{-70pt}
$
\diag{adjs-Delta*}
$
\newpage
% _ _ _ __
% / \ __| |(_)___ / _|
% / _ \ / _` || / __| | |_
% / ___ \ (_| || \__ \ | _|
% /_/ \_\__,_|/ |___/ |_|
% |__/
%
% «adjoints-f» (to ".adjoints-f")
Adjoints to $(y:=f(x))^*$ can be built using quantifiers and equality:
\def\Px{Px}
\def\Qx{Qx}
\def\Ry{Ry}
\def\Sy{Sy}
\def\Rfx{Rfx}
\def\Sfx{Sfx}
\def\Tx{Txy}
\def\Ux{Uxy}
\def\Exx{∃x.}
\def\Fax{∃x.}
\def\fxy{fx{=}y}
\def\fxfx{fx{=}fx}
\bsk
%:
%:
%:
%: [\fxy∧\Px]^1
%: ------------
%: [\fxy∧\Px]^1 \Px
%: ------------ :::α
%: \fxy \Qx
%: -----------------
%: \fxy∧\Qx
%: ------------
%: \Exy\fxy∧\Px \Exx\fxy∧\Qx
%: ----------------------------1
%: \Exx\fxy∧\Qx
%:
%: ^Sigmaf-F
%:
%:
%:
%:
%:
%: [\fxy∧\Qx]^1
%: ------------
%: [\fxy∧\Qx]^1 \Exx\fxy∧\Qx
%: ----- ------------ :::
%: \fxfx \Qx \fxy \Ry
%: ---------- -------------------
%: \fxfx∧\Qx \Rfx
%: -----------------[y:=fx];1
%: \Rfx
%:
%: ^Sigmaf-transposeleft
%:
%: [\fxy∧\Qx]^1
%: ------------
%: [\fxy∧\Qx]^1 \Qx
%: ------------ ::::f
%: \fxy \Rfx
%: --------------
%: \Exx\fxy∧\Qx \Ry
%: ---------------------1
%: \Ry
%:
%: ^Sigmaf-transposeright
%:
%:
%:
%: [\Ry]^1
%: :::::β
%: \Rfx \Sy
%: ----------[y:=fx]^1
%: \Sfx
%:
%: ^fstar-F
%:
%:
%: [\Sy]^1
%: ::::::::::::h
%: \Fay\fxy⊸\Tx
%: ------------
%: \Sfx \fxy⊸\Tx
%: ----- ------------------[y:=fx];1
%: \fxfx \fxfx⊸\Tx
%: ---------------------
%: \Tx
%:
%: ^Pif-transposeleft
%:
%:
%: [\fxy]^1 [\Sy]^2
%: ----------------
%: Sfx
%: :::
%: Tx
%: --------1
%: \Sy \fxy⊸\Tx
%: -------------2
%: \Fax\fxy⊸\Tx
%:
%: ^Pif-transposeright
%:
%:
%: [\fxy]^1 [\fxy⊸\Tx]^2
%: ----------------------
%: \Tx
%: :::γ
%: \Ux
%: --------1
%: \Fax\fxy⊸\Tx \fxy⊸\Ux
%: -----------------------2
%: \Fax\fxy⊸\Ux
%:
%: ^Pif-F
%:
\def\Pxy{Pxy}
\def\Qxy{Qxy}
\def\Rx {Rx}
\def\Sx {Sx}
\def\Tx {Tx}
\def\Ux {Ux}
\def\Exy{∃y.}
\def\Fay{∀y.}
%D diagram adjs-f*
%D 2Dx 100 +40
%D 2D 100 A0 |-> A1
%D 2D | |
%D 2D | |-> |
%D 2D | |
%D 2D +25 A2 |-> A3
%D 2D | |
%D 2D | <-> |
%D 2D | |
%D 2D +25 B0 <-| B1
%D 2D | |
%D 2D | <-| |
%D 2D | |
%D 2D +25 B2 <-| B3
%D 2D | |
%D 2D | <-> |
%D 2D | |
%D 2D +25 C0 |-> C1
%D 2D | |
%D 2D | |-> |
%D 2D | |
%D 2D +25 C2 |-> C3
%D 2D
%D 2D +20 D0 <=> D1
%D 2D
%D 2D +20 E0 |-> E1
%D 2D +10 E2 --> E3
%D 2D
%D ren A0 A1 ==> \Px \Exx\fxy∧\Px
%D ren A2 A3 ==> \Qx \Exx\fxy∧\Qx
%D ren B0 B1 ==> \Rfx \Ry
%D ren B2 B3 ==> \Sfx \Sy
%D ren C0 C1 ==> \Tx \Exx\fxy⊸\Tx
%D ren C2 C3 ==> \Ux \Exx\fxy⊸\Ux
%D ren D0 D1 ==> 𝐛P(X) 𝐛P(Y)
%D ren E0 E1 ==> x fx
%D ren E2 E3 ==> X Y
%D
%D (( A0 A1 |->
%D A2 A3 |->
%D B0 B1 <-|
%D B2 B3 <-|
%D C0 C1 |->
%D C2 C3 |->
%D A0 A3 harrownodes nil 20 nil |->
%D A2 B1 harrownodes nil 20 nil |-> sl^
%D A2 B1 harrownodes nil 20 nil <-| sl_
%D B0 B3 harrownodes nil 20 nil <-|
%D B2 C1 harrownodes nil 20 nil <-| sl^
%D B2 C1 harrownodes nil 20 nil |-> sl_
%D C0 C3 harrownodes nil 20 nil |->
%D A0 A2 -> .plabel= l α
%D A1 A3 -> .plabel= r Σ_πα
%D A2 B0 -> .plabel= l \sm{f\\(Σ_π^♯)g}
%D A3 B1 -> .plabel= r \sm{(Σ_π^♭)f\\g}
%D B0 B2 -> .plabel= l π^*β
%D B1 B3 -> .plabel= r β
%D B2 C0 -> .plabel= l \sm{(Π_π^♭)h\\k}
%D B3 C1 -> .plabel= r \sm{h\\(Π_π^♯)k}
%D C0 C2 -> .plabel= l γ
%D C1 C3 -> .plabel= r Π_πγ
%D D0 D1 -> sl^^ .plabel= a Σ_f
%D D0 D1 <- .plabel= m f^*
%D D0 D1 -> sl__ .plabel= b Π_f
%D E0 E1 |->
%D E2 E3 -> .plabel= a π
%D
%D A1 A3 midpoint relplace 70 0 Σ_πα:=\pdedscale{0.40}{Sigmaf-F}
%D A3 B1 midpoint relplace 70 0 (Σ_π^♭)f:=\pdedscale{0.40}{Sigmaf-transposeright}
%D A2 B0 midpoint relplace - 0 (Σ_π^♯)g:=\pdedscale{0.40}{Sigmaf-transposeleft}
%D B0 B2 midpoint relplace -50 0 π^*β:=\pdedscale{0.55}{fstar-F}
%D B2 C0 midpoint relplace -60 0 (Π_π^♭)h:=\pdedscale{0.40}{Pif-transposeleft}
%D B3 C1 midpoint relplace 55 0 (Π_π^♯)k:=\pdedscale{0.40}{Pif-transposeright}
%D C1 C3 midpoint relplace 70 0 Π_πγ:=\pdedscale{0.40}{Pif-F}
%D ))
%D enddiagram
%D
\pu
\phantom{a}
\hspace{-75pt}
$
\diag{adjs-f*}
$
%\printbibliography
\end{document}
% __ __ _
% | \/ | __ _| | _____
% | |\/| |/ _` | |/ / _ \
% | | | | (_| | < __/
% |_| |_|\__,_|_|\_\___|
%
% <make>
* (eepitch-shell)
* (eepitch-kill)
* (eepitch-shell)
# (find-LATEXfile "2019planar-has-1.mk")
make -f 2019.mk STEM=2020seelyhyp-poster veryclean
make -f 2019.mk STEM=2020seelyhyp-poster pdf
% Local Variables:
% coding: utf-8-unix
% ee-tla: "shp"
% End: