% (find-LATEX "2026jacobs.tex") % (defun c () (interactive) (find-LATEXsh "lualatex -record 2026jacobs.tex" :end)) % (defun C () (interactive) (find-LATEXsh "lualatex 2026jacobs.tex" "Success!!!")) % (defun D () (interactive) (find-pdf-page "~/LATEX/2026jacobs.pdf")) % (defun d () (interactive) (find-pdftools-page "~/LATEX/2026jacobs.pdf")) % (defun e () (interactive) (find-LATEX "2026jacobs.tex")) % (defun o () (interactive) (find-LATEX "2026jacobs.tex")) % (defun u () (interactive) (find-latex-upload-links "2026jacobs")) % (defun v () (interactive) (find-2a '(e) '(d))) % (defun d0 () (interactive) (find-ebuffer "2026jacobs.pdf")) % (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g)) % (defun oe () (interactive) (find-2a '(o) '(e))) % (code-eec-LATEX "2026jacobs") % (find-pdf-page "~/LATEX/2026jacobs.pdf") % (find-sh0 "cp -v ~/LATEX/2026jacobs.pdf /tmp/") % (find-sh0 "cp -v ~/LATEX/2026jacobs.pdf /tmp/pen/") % (find-xournalpp "/tmp/2026jacobs.pdf") % file:///home/edrx/LATEX/2026jacobs.pdf % file:///tmp/2026jacobs.pdf % file:///tmp/pen/2026jacobs.pdf % http://anggtwu.net/LATEX/2026jacobs.pdf % https://anggtwu.net/LATEX/2026jacobs.pdf % (find-LATEX "2019.mk") % (find-Deps1-links "Caepro5 Piecewise2 Maxima2") % (find-Deps1-cps "Caepro5 Piecewise2 Maxima2") % (find-Deps1-anggs "Caepro5 Piecewise2 Maxima2") % (find-MM-aula-links "2026jacobs" "2" "jac2026" "jac") % «.geometry» (to "geometry") % «.edrx26a» (to "edrx26a") % «.biber» (to "biber") % «.edrx26b» (to "edrx26b") % «.edrx26c» (to "edrx26c") % «.defs» (to "defs") % «.footer» (to "footer") % «.defs-T-and-B» (to "defs-T-and-B") % % «.title» (to "title") % «.toc» (to "toc") % «.links» (to "links") % «.cartesianness-jacobs» (to "cartesianness-jacobs") % «.cartesianness-edrx» (to "cartesianness-edrx") % «.fibred-equality» (to "fibred-equality") % «.BCC-equality» (to "BCC-equality") % % «.writetoc» (to "writetoc") % «.references» (to "references") % «.make-with-bib» (to "make-with-bib") % ;-- defs \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-LATEX "dednat7-test1.tex") %\usepackage{proof} % For derivation trees ("%:" lines) \input diagxy % For 2D diagrams ("%D" lines) %\xyoption{curve} % For the ".curve=" feature in 2D diagrams % % «geometry» (to ".geometry") % (find-es "tex" "geometry") \usepackage[a6paper, landscape, top=1.5cm, bottom=.25cm, left=1cm, right=1cm, includefoot ]{geometry} % % «edrx26a» (to ".edrx26a") \usepackage{edrx26a} % (find-LATEX "edrx26a.sty") % % «biber» (to ".biber") \usepackage[backend=biber, style=alphabetic]{biblatex} % (find-es "tex" "biber") \addbibresource{catsem-ab.bib} % (find-LATEX "catsem-ab.bib") \addbibresource{education.bib} % (find-LATEX "education.bib") % \begin{document} % «edrx26b» (to ".edrx26b") \input edrx26b.tex % (find-LATEX "edrx26b.tex") % «edrx26c» (to ".edrx26c") % (find-LATEX "edrx26c.tex") %L processsubfile "edrx26c.tex" -- runs the "%L"s \input edrx26c % loads the defs % «defs» (to ".defs") % (find-LATEX "edrx21defs.tex" "colors") % (find-LATEX "edrx21.sty") % «footer» (to ".footer") % (find-LATEX "edrxheadfoot.tex") \def\drafturl{http://anggtwu.net/LATEX/2026-1-C2.pdf} \def\drafturl{http://anggtwu.net/2026.1-C2.html} \def\draftfooter{\tiny \href{\drafturl}{\jobname{}} \ColorBrown{\shorttoday{} \hours}} % «defs-T-and-B» (to ".defs-T-and-B") \long\def\ColorDarkOrange#1{{\color{orange!90!black}#1}} \def\T(Total: #1 pts){{\bf(Total: #1)}} \def\T(Total: #1 pts){{\bf(Total: #1 pts)}} \def\T(Total: #1 pts){\ColorRed{\bf(Total: #1 pts)}} \def\B (#1 pts){\ColorDarkOrange{\bf(#1 pts)}} \def\Eq {\mathsf{Eq}} \def\BCCL {\mathsf{BCCL}} % ;-- title % _____ _ _ _ % |_ _(_) |_| | ___ _ __ __ _ __ _ ___ % | | | | __| |/ _ \ | '_ \ / _` |/ _` |/ _ \ % | | | | |_| | __/ | |_) | (_| | (_| | __/ % |_| |_|\__|_|\___| | .__/ \__,_|\__, |\___| % |_| |___/ % % «title» (to ".title") % (jac2026p 1 "title") % (jac2026a "title") \thispagestyle{empty} \begin{center} \vspace*{1.2cm} {\bf \Large Notes about Jacobs's book} \bsk %Aula nn: ponha o título aqui % %\bsk Eduardo Ochs - RCN/PURO/UFF Psicopata do CEFET \url{https://anggtwu.net/math-b.html} \end{center} %\newpage % ;-- toc % «toc» (to ".toc") % (to "writetoc") % ;-- links % «links» (to ".links") % (jac2026p 2 "links") % (jac2026a "links") %{\bf Links} % %\scalebox{0.6}{\def\colwidth{16cm}\firstcol{ %}\anothercol{ %}} % (jac2020p) % (jac2020a) % (find-books "__cats/__cats.el" "freyd76") % (find-books "__cats/__cats.el" "freyd-scedrov" "28" "1.39. The language of diagrams") % (find-books "__cats/__cats.el" "heller-tierney" "55" "Freyd") % (misp 17 "freyd-notation") % (misa "freyd-notation") % (misa "freyd-notation" "equalizers") % (misp 18 "freyd-with-functors") % (misa "freyd-with-functors") % (misp 44 "ness") % (misa "ness") \newpage %-- cartesianness-jacobs % % ____ _ _ _ % / ___|__ _ _ __| |_ | | __ _ ___ ___ | |__ ___ % | | / _` | '__| __| _ | |/ _` |/ __/ _ \| '_ \/ __| % | |__| (_| | | | |_ | |_| | (_| | (_| (_) | |_) \__ \ % \____\__,_|_| \__| \___/ \__,_|\___\___/|_.__/|___/ % % «cartesianness-jacobs» (to ".cartesianness-jacobs") % (jac2026p 99 "cartesianness-jacobs") % (jac2026a "cartesianness-jacobs") % (find-books "__cats/__cats.el" "jacobs" "27" "Finally, we come to the definition of 'fibration'") \SLIDE{Cartesianness (Jacobs)} \scalebox{0.8}{\def\colwidth{14cm}\firstcol{ From \cite[p.27]{Jacobs}: \ssk {\bf 1.1.3. Definition.} Let $p:\bbE→\bbB$ be a functor. (i) A morphism $f:X→Y$ in $\bbE$ is {\bf Cartesian over} $u:I→J$ in $\bbB$ if $pf=u$ and every $g:Z→Y$ in $\bbE$ for which one has $pg=u∘w$ for some $w:pZ→I$, uniquely determines an $h:Z→X$ in $\bbE$ above $w$ with $f∘h=g$. In a diagram: % %L forths["-"] = function () pusharrow("-") end % %D diagram cartesianness-jacobs %D 2Dx 100 +20 +20 +30 %D 2D 100 A0 ____ %D 2D +15 E \ \ %D 2D +10 | A1 - A2 %D 2D | %D 2D +10 v A3 ____ %D 2D +15 B \ \ %D 2D +10 A4 - A5 %D %D ren E B A0 A1 A2 A3 A4 A5 ==> \bbE \bbB Z X Y pZ I J %D %D (( E B -> .plabel= l p %D %D A0 A1 --> .plabel= l h %D A1 A2 -> .plabel= b f %D A0 A2 -> .plabel= a g %D A3 A4 -> .plabel= l w %D A4 A5 -> .plabel= b u %D A3 A5 -> .plabel= a u∘w=pg %D )) %D enddiagram \pu $$\diag{cartesianness-jacobs} $$ We call $f:X→Y$ in the total category $\bbE$ Cartesian if it is Cartesian over its underlying map $pf$ in $\bbB$. }\anothercol{ }} \newpage %-- cartesianness-edrx % ____ _ _____ _ % / ___|__ _ _ __| |_ | ____|__| |_ ____ __ % | | / _` | '__| __| | _| / _` | '__\ \/ / % | |__| (_| | | | |_ | |__| (_| | | > < % \____\__,_|_| \__| |_____\__,_|_| /_/\_\ % % «cartesianness-edrx» (to ".cartesianness-edrx") % (jac2026p 99 "cartesianness-edrx") % (jac2026a "cartesianness-edrx") \SLIDE{Cartesianness (Edrx)} %L forths["-"] = function () pusharrow("-") end % %D diagram cartesianness-edrx %D 2Dx 100 +00 +20 +15 +15 +10 +20 +15 +15 +10 +20 %D 2D 100 U0 U1 %D 2D | | %D 2D +10 A0 ____ | B0 ____ | C0 ____ %D 2D \ \ | \ \ | \ \ %D 2D +15 A1 - A2 | B1 - B2 | C1 - C2 %D 2D | | %D 2D +10 A3 ____ | B3 ____ | C3 ____ %D 2D \ \ | \ \ | \ \ %D 2D +15 A4 - A5 | B4 - B5 | C4 - C5 %D 2D | | %D 2D +10 L0 L1 %D %D ren A0 A1 A2 A3 A4 A5 ==> {} Q R {} {} {} %D ren U0 L0 B0 B1 B2 B3 B4 B5 ==> ∀ {} P Q R A B C %D ren U1 L1 C0 C1 C2 C3 C4 C5 ==> ∃! {} P Q R A B C %D %D (( A1 A2 -> .plabel= a β %D %D U0 L0 - %D %D # B0 B1 -> .plabel= l α %D B1 B2 -> .plabel= b β %D B0 B2 -> .plabel= a γ %D B3 B4 -> .plabel= l f %D B4 B5 -> .plabel= b g %D B3 B5 -> .plabel= a h %D %D U1 L1 - %D %D C0 C1 -> .plabel= l α %D C1 C2 -> .plabel= b β %D C0 C2 -> .plabel= a γ %D C3 C4 -> .plabel= l f %D C4 C5 -> .plabel= b g %D C3 C5 -> .plabel= a h %D )) %D enddiagram \pu \scalebox{0.8}{\def\colwidth{9cm}\firstcol{ Let $p:\bbE \to \bbB$ be our projection functor. $β:Q→R$ is {\sl cartesian} when: % $$\diag{cartesianness-edrx} $$ The details: % $$∀\pmat{P,A,B,C, γ,f,g,h,\\ A=pP,B=pQ,C=pR,\\ g=pβ,h=pγ,h=g∘f }. ∃!\pmat{α,\\ γ=β∘α,\\ f=pα} $$ }\anothercol{ }} \newpage %-- fibred-equality % «fibred-equality» (to ".fibred-equality") % (jac2026p 99 "fibred-equality") % (jac2026a "fibred-equality") % (find-books "__cats/__cats.el" "jacobs" "190" "3.4. Fibred equality") \SLIDE{Fibred equality} \sa {} {〈\id,π'〉} \sa {IJ} {I×J} \sa {KJ} {K×J} \sa {IJJ} {(I×J)×J} \sa {KJJ} {(K×J)×J} \sa {EIJ} {\bbE_{I×J}} \sa {EIJJ} {\bbE_{(I×J)×J}} \sa {dd(I,J)} {{δ(I,J)}} \sa {dd(K,J)} {{δ(K,J)}} \sa {dd(I,J)*} {{δ(I,J)^*}} \sa {dd(K,J)*} {{δ(K,J)^*}} \sa {Eq(I,J)} {{\Eq(I,J)}} \sa {Eq(K,J)} {{\Eq(K,J)}} \sa {Eq_IJ} {{\Eq_{I,J}}} \sa {Eq_KJ} {{\Eq_{K,J}}} \sa {Ud(I,J)} {{\coprod_\ga{dd(I,J)}}} \sa {UE(I,J)} {\mat{\ga {Eq_IJ} P =\\ \ga {Ud(I,J)} P }} %D diagram p190-Eq %D 2Dx 100 +65 +40 +60 %D 2D 100 A0 |-> A1 B0 |-> B1 %D 2D | | | | %D 2D v v v v %D 2D +30 A2 <-| A3 B2 <-| B3 %D 2D %D 2D +20 EIJ <=> EIJJ %D 2D +20 IJ --> IJJ IJ' --> IJJ' %D 2D %D ren A0 A1 ==> P \ga{UE(I,J)} %D ren A2 A3 ==> \ga{dd(I,J)*}Q Q %D ren IJ IJJ ==> \ga{IJ} \ga{IJJ} %D ren EIJ EIJJ ==> \ga{EIJ} \ga{EIJJ} %D %D ren B0 B1 ==> P(i,j) j{=}j'∧P(i,j) %D ren B2 B3 ==> Q(i,j,j) Q(i,j,j') %D ren IJ' IJJ' ==> \ga{IJ} \ga{IJJ} %D %D (( A0 A1 |-> %D A2 A3 <-| %D A0 A3 harrownodes nil 20 nil <-> %D A0 A2 -> %D A1 A3 -> %D %D EIJ EIJJ -> sl^ .plabel= a \ga{Eq_IJ}=\ga{Ud(I,J)} %D EIJ EIJJ <- sl_ .plabel= b \ga{dd(I,J)*} %D IJ IJJ -> .plabel= a \ga{dd(I,J)}=\ga{} %D %D B0 B1 |-> %D B2 B3 <-| %D B0 B3 harrownodes nil 20 nil <-> %D B0 B2 -> %D B1 B3 -> %D %D IJ' IJJ' -> .plabel= a (i,j)↦((i,j),j) %D )) %D enddiagram \pu \scalebox{0.9}{\def\colwidth{9cm}\firstcol{ \vspace*{0.1cm} {\bf 3.4. Fibred equality} (From {\cite[p.190]{Jacobs}}): % $$\diag{p190-Eq} $$ }\anothercol{ }} \newpage %-- BCC-equality % «BCC-equality» (to ".BCC-equality") % (jac2026p 99 "BCC-equality") % (jac2026a "BCC-equality") \SLIDE{Beck-Chevally for equality} %D diagram TP %D 2Dx 100 %D 2D 100 B4 %D 2D ^ %D 2D | %D 2D v %D 2D +20 B6 %D 2D %D 2D EKJJ %D 2D %D 2D +15 KJJ %D 2D %D ren B4 B6 ==> \ga{Eq(K,J)}{f'}^*P f^*\ga{Eq(I,J)}P %D # ren EKJJ ==> \bbE_{(K×J)×J} %D ren KJJ ==> (K×J)×J %D %D (( B4 B6 -> sl_ .plabel= l ♮ %D B4 B6 <- sl^ .plabel= r \BCCL %D # EKJJ place %D KJJ place %D )) %D enddiagram \pu \sa{width1}{9cm} \sa{width2}{7cm} \scalebox{0.6}{\def\colwidth{\ga{width1}}\firstcol{ {} From \cite[p.191]{Jacobs}: ...the Beck-Chevalley condition holds: for each map $u:K→I$ in $\bbB$ (between the parameter objects) the canonical natural transformation % $$\ga{Eq(K,J)} (u×\id)^* \Longrightarrow ((u×\id)×\id)^* \ga{Eq(I,J)}$$ % is an isomorphism. \bsk In the diagrams of the following pages we have $f' = u×\id$ and $f = (u×\id)×\id$, so the canonical natural transformation above is: % $$T : \ga{Eq(K,J)} {f'}^* \Longrightarrow f^* \ga{Eq(I,J)}$$ If we apply it to an object $P$ we get the morphism % $$TP : \ga{Eq(K,J)} {f'}^* P \to f^* \ga{Eq(I,J)} P$$ in the fiber $\bbE_{(K×J)×J}$, that is drawn as `$♮$' in my diagrams -- as in the column at the right. }\def\colwidth{\ga{width2}}\anothercol{ {} $$\scalebox{2.0}{$ \diag{TP} $} $$ }} \sa {B0} {B0} \sa {B1} {B1} \sa {B2} {B2} \sa {B2'} {B2'} \sa {B3} {B3} \sa {B4} {B4} \sa {B5} {B5} \sa {B6} {B6} \sa {B7} {B7} \sa {b0} {b0} \sa {b1} {b1} \sa {b2} {b2} \sa {b3} {b3} \sa {f} {f} \sa {f'} {f'} \sa {z} {z} \sa {z'} {z'} %D diagram BCCL-generic %D 2Dx 100 +70 +70 +70 %D 2D 100 B0 <====================== B1 %D 2D -\\ -\\ %D 2D | \\ | \\ %D 2D v \\ v \\ %D 2D +20 B2 <\\> B2' ============== B3 \\ %D 2D /\ \/ /\ \/ %D 2D +15 \\ B4 \\ B5 %D 2D \\ - \\ - %D 2D \\ | \\| %D 2D \\v \v %D 2D +20 B6 <===================== B7 %D 2D %D 2D +10 b0 |---------------------> b1 %D 2D |-> |-> %D 2D +35 b2 |--------------------> b3 %D 2D %D ren B0 B1 ==> \ga{B0} \ga{B1} %D ren B2 B2' B3 ==> \ga{B2} \ga{B2'} \ga{B3} %D ren B4 B5 ==> \ga{B4} \ga{B5} %D ren B6 B7 ==> \ga{B6} \ga{B7} %D ren b0 b1 ==> \ga{b0} \ga{b1} %D ren b2 b3 ==> \ga{b2} \ga{b3} %D (( %D B0 B1 <-| B0 B2 -> B0 B2' -> B1 B3 -> B2 B2' <-> B2' B3 <-| %D B0 B4 |-> B1 B5 |-> %D B2 B6 <-| B3 B7 <-| %D B6 B7 <-| B5 B7 -> .plabel= r \id %D B4 B6 -> sl_ .plabel= l ♮ B4 B6 <- sl^ .plabel= r \BCCL %D B0 B2' midpoint B1 B3 midpoint harrownodes nil 20 nil <-| %D B0 B2 midpoint B4 B6 midpoint dharrownodes nil 20 nil |-> %D B1 B3 midpoint B5 B7 midpoint dharrownodes nil 20 nil <-| %D )) %D (( %D b0 b1 -> .plabel= b \ga{f'} %D b0 b2 -> .plabel= l \ga{z'} %D b1 b3 -> .plabel= r \ga{z} %D b2 b3 -> .plabel= a \ga{f} %D b0 relplace 20 7 \pbsymbol{7} %D )) %D enddiagram \pu \sa {BCCL-equality-jacobs} {{ % \sa {B1} {P} \sa {B5} {\ga{Eq_IJ} P} \sa {B7} {\ga{Eq_IJ} P} \sa {B3} {z^* \ga{Eq_IJ} P} \sa {B2'} {{f'}^* z^* \ga{Eq_IJ} P} % \sa {B6} {f^* \ga{Eq_IJ} P} \sa {B2} {{z'}^* f^* \ga{Eq_IJ} P} % \sa {B0} {{f'}^* P} \sa {B4} {\ga{Eq_KJ} {f'}^* P} % \sa {b0} {\ga{KJ}} \sa {b1} {\ga{IJ}} \sa {b2} {\ga{KJJ}} \sa {b3} {\ga{IJJ}} % \sa {f'} {f' = u×\id} \sa {z} {z = \ga{dd(I,J)}} \sa {z'} {z' = \ga{dd(K,J)}} \sa {f} {f = (u×\id)×\id} % \diag{BCCL-generic} }} \sa {BCCL-equality-edrx} {{ % \sa {B1} {P(i,j)} \sa {B5} {j{=}j' ∧ P(i,j)} \sa {B7} {j{=}j' ∧ P(i,j)} \sa {B3} {j{=}j ∧ P(i,j)} \sa {B2'} {j{=}j ∧ P(u(k),j)} % \sa {B6} {j{=}j' ∧ P(u(k),j)} \sa {B2} {j{=}j ∧ P(u(k),j)} % \sa {B0} {P(u(k),j)} \sa {B4} {j{=}j' ∧ P(u(k),j)} % \sa {b0} {\ga{KJ}} \sa {b1} {\ga{IJ}} \sa {b2} {\ga{KJJ}} \sa {b3} {\ga{IJJ}} % \sa {f'} { (k,j) ↦ (u(k),j)} \sa {z} {\;\; (i,j) ↦ ((i,j),j)} \sa {z'} { (k,j) ↦ ((k,j),j) \;\;} \sa {f} {((k,j),j') ↦ ((u(k),j),j')} % \diag{BCCL-generic} }} \scalebox{0.58}{\def\colwidth{18cm}\firstcol{ \vspace*{-2cm} $$\ga{BCCL-equality-jacobs} $$ \bsk $$\ga{BCCL-equality-edrx} $$ \vspace*{-2cm} }\anothercol{ }} %D diagram BCCL-std %D 2Dx 100 +45 +55 +45 %D 2D 100 B0 <====================== B1 %D 2D -\\ -\\ %D 2D | \\ | \\ %D 2D v \\ v \\ %D 2D +20 B2 <\\> B2' ============== B3 \\ %D 2D /\ \/ /\ \/ %D 2D +15 \\ B4 \\ B5 %D 2D \\ - \\ - %D 2D \\ | \\| %D 2D \\v \v %D 2D +20 B6 <===================== B7 %D 2D %D 2D +10 b0 |---------------------> b1 %D 2D |-> |-> %D 2D +35 b2 |--------------------> b3 %D 2D %D (( %D B0 .tex= f^{\prime*}P B1 .tex= P %D B2 .tex= z^{\prime*}f^*Σ_zP B2' .tex= f^{\prime*}z^*Σ_zP B3 .tex= z^*Σ_zP %D B4 .tex= Σ_{z'}f^{\prime*}P B5 .tex= Σ_zP %D B6 .tex= f^*Σ_zP B7 .tex= Σ_zP %D B0 B1 <-| B0 B2 -> B0 B2' -> B1 B3 -> B2 B2' <-> B2' B3 <-| %D B0 B4 |-> B1 B5 |-> %D B2 B6 <-| B3 B7 <-| %D B6 B7 <-| B5 B7 -> .plabel= r \id %D B4 B6 -> sl_ .plabel= l ♮ B4 B6 <- sl^ .plabel= r \BCCL %D B0 B2' midpoint B1 B3 midpoint harrownodes nil 20 nil <-| %D B0 B2 midpoint B4 B6 midpoint dharrownodes nil 20 nil |-> %D B1 B3 midpoint B5 B7 midpoint dharrownodes nil 20 nil <-| %D )) %D (( b0 .tex= X×_{Y}Z b1 .tex= Z b2 .tex= X b3 .tex= Y %D b0 b1 -> .plabel= b f' %D b0 b2 -> .plabel= l z' %D b1 b3 -> .plabel= r z %D b2 b3 -> .plabel= a f %D b0 relplace 20 7 \pbsymbol{7} %D )) %D enddiagram \pu $$\diag{BCCL-std}$$ % ;-- writetoc % «writetoc» (to ".writetoc") \directlua{toclines:writetoc()} % Writes in: (find-LATEXfile "2026jacobs.mytoc") % See: (to "toc") % ;-- references % «references» (to ".references") \printbibliography % ;-- write-dnt-file % «write-dnt-file» (to ".write-dnt-file") % (find-fline "~/LATEX/" "2026jacobs.dnt") % (find-fline "~/LATEX/2026jacobs.dnt") %L write_dnt_file ("2026jacobs.dnt") \pu \GenericWarning{Success:}{Success!!!} % Used by `M-x cv' \end{document} % (find-pdfpages2-links "~/LATEX/" "2026jacobs") % ;-- make-with-bib % «make-with-bib» (to ".make-with-bib") % (wiya "make-with-bib")  (eepitch-shell)  (eepitch-kill)  (eepitch-shell) cd ~/LATEX/ # which biber # biber --version make -f 2019.mk STEM=2026jacobs veryclean lualatex 2026jacobs.tex biber 2026jacobs lualatex 2026jacobs.tex # (find-pdf-page "~/LATEX/2026jacobs.pdf") % Local Variables: % coding: utf-8-unix % outline-regexp: "% +;--" % ee-tla: "jac" % ee-tla: "jac2026" % End: