From 1317daa802599d0cd3ba08e395bc6bc66bf5b703 Mon Sep 17 00:00:00 2001 From: Leon Vatthauer Date: Wed, 27 Mar 2024 10:35:12 +0100 Subject: [PATCH] Export macros to catprog.sty, work on F-algebras section --- tex/.vscode/ltex.dictionary.en-US.txt | 6 + tex/.vscode/settings.json | 4 +- tex/catprog.sty | 221 +++++++++++ tex/main.pdf | Bin 131300 -> 148676 bytes tex/main.tex | 22 +- tex/sections/01_introduction.tex | 40 +- tex/sections/02_categories.tex | 520 +++++++++++++++++++------- 7 files changed, 651 insertions(+), 162 deletions(-) create mode 100644 tex/catprog.sty diff --git a/tex/.vscode/ltex.dictionary.en-US.txt b/tex/.vscode/ltex.dictionary.en-US.txt index 20768bc..a171c7f 100644 --- a/tex/.vscode/ltex.dictionary.en-US.txt +++ b/tex/.vscode/ltex.dictionary.en-US.txt @@ -37,3 +37,9 @@ monoids n-ary Cocartesian Yoneda +endofunctor +F-Coalgebras +Corecursion +Coinduction +Colimits +Colimit diff --git a/tex/.vscode/settings.json b/tex/.vscode/settings.json index 3659725..7116be1 100644 --- a/tex/.vscode/settings.json +++ b/tex/.vscode/settings.json @@ -27,6 +27,8 @@ "ltex.latex.commands": { "\\customlabel{}": "ignore", "\\setminted[]{}": "ignore", - "\\setmintedinline[]{}": "ignore" + "\\setmintedinline[]{}": "ignore", + "\\setmathfont[]{}": "ignore", + "\\setmathfont{}": "ignore" } } \ No newline at end of file diff --git a/tex/catprog.sty b/tex/catprog.sty new file mode 100644 index 0000000..ac3094d --- /dev/null +++ b/tex/catprog.sty @@ -0,0 +1,221 @@ +% +% Standard macros to typeset papers on category theory and semantics +% +% Unless \catname is defined, make it bold. +% So, call \providecommand{\catname}{\mathcal} +% or \reprovidecommand{\catname}{\mathcal} +% before calling this file if you prefer calligraphic names for categories. +% +% Same applies to other commands. +% +% COPIED FROM https://gitlab.cs.fau.de/i8/TexCommon/ AND THEN ADJUSTED. + +\RequirePackage{bm} % Needed for defbbname +\RequirePackage{mathtools} % Needed for coloneqq + +\providecommand{\catname}{\mathsf} +%\providecommand{\mndname}{\mathbbb} +\providecommand{\clsname}{\mathscr} +\providecommand{\oname}[1]{\operatorname{\mathsf{#1}}} + +%% Defining category names like \BA, \BB, etc +\def\defcatname#1{\expandafter\def\csname B#1\endcsname{\catname{#1}}} +\def\defcatnames#1{\ifx#1\defcatnames\else\defcatname#1\expandafter\defcatnames\fi} +\defcatnames ABCDEFGHIJKLMNOPQRSTUVWXYZ\defcatnames + +%% Defining \CA, \CB, etc +\def\defclsname#1{\expandafter\def\csname C#1\endcsname{\clsname{#1}}} +\def\defclsnames#1{\ifx#1\defclsnames\else\defclsname#1\expandafter\defclsnames\fi} +\defclsnames ABCDEFGHIJKLMNOPQRSTUVWXYZ\defclsnames + +%% Defining \BBA, \BBB, etc +\def\defbbname#1{\expandafter\def\csname BB#1\endcsname{{\bm{\mathsf{#1}}}}} +\def\defbbnames#1{\ifx#1\defbbnames\else\defbbname#1\expandafter\defbbnames\fi} +\defbbnames ABCDEFGHIJKLMNOPQRSTUVWXYZ\defbbnames + +%% Defining \BMA, \BMB, etc +\def\defbbname#1{\expandafter\def\csname BM#1\endcsname{{\bm{\mathsf{#1}}}}} +\def\defbbnames#1{\ifx#1\defbbnames\else\defbbname#1\expandafter\defbbnames\fi} +\defbbnames ABCDEFGHIJKLMNOPQRSTUVWXYZ\defbbnames + +%% Some standard categories +\def\Set{\ensuremath{\catname{Set}}} +\def\Par{\ensuremath{\catname{Par}}} +\def\Rel{\ensuremath{\catname{Rel}}} +\def\Cpo{\ensuremath{\catname{Cpo}}} +\def\Pos{\ensuremath{\catname{Pos}}} +\def\Mon{\ensuremath{\catname{Mon}}} +\def\Gra{\ensuremath{\catname{Gra}}} +\providecommand{\Alg}[1]{\ensuremath{\catname{Alg}(#1)}} +%% Objects of category +\providecommand{\obj}[1]{\ensuremath{\vert #1 \vert}} +%% Dual category +\providecommand{\dual}[1]{\ensuremath{#1^{op}}} + +% Misc +%% Commutation of diagrams +\providecommand{\comm}{\circlearrowleft} +%% Banana brackets for catamorphisms +\RequirePackage{stmaryrd} +\providecommand{\cata}[1]{\llparenthesis #1 \rrparenthesis} + + +\providecommand{\eps}{{\operatorname\epsilon}} +\providecommand{\amp}{\mathbin{\&}} + +\providecommand{\argument}{\operatorname{-\!-}} +\providecommand{\altargument}{\underline{\;\;}} + +\providecommand{\wave}[1]{\widetilde{#1}} % Overline wave +\providecommand{\ul}{\underline} % Underline + +\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf} +\providecommand{\mplus}{{\scriptscriptstyle\bf+}} % Small '+' for indexing + +\providecommand{\smin}{\smallsetminus} + +\providecommand{\ass}{\mathrel{\coloneqq}} +\providecommand{\bnf}{\mathrel{\Coloneqq}} + +%% Some standard functors +\providecommand{\PSet}{{\mathcal P}} % Powerset +\providecommand{\FSet}{{\mathcal P}_{\omega}} % Finite powerset +\providecommand{\CSet}{{\mathcal P}_{\omega_1}} % Countable powerset +\providecommand{\NESet}{{\mathcal P}^{\mplus}} % Non-empty powerset +\providecommand{\Id}{\operatorname{Id}} + +%% General categorical notation +\providecommand{\Hom}{\mathsf{Hom}} +\providecommand{\id}{\mathsf{id}} +\providecommand{\op}{\mathsf{op}} +\providecommand{\comp}{\mathbin{\circ}} +\providecommand{\iso}{\mathbin{\cong}} +\providecommand{\tensor}{\mathbin{\otimes}} +\providecommand{\unit}{\star} +\providecommand{\bang}{\operatorname!} % Initial/final map + +%% Various arrows +\providecommand{\from}{\leftarrow} + +\providecommand{\ito}{\hookrightarrow} % Injection +\providecommand{\ifrom}{\hookleftarrow} + +\providecommand{\pto}{\mathrel{\rightharpoonup}} % Partial function +\providecommand{\pfrom}{\mathrel{\leftarpoonup}} % + +\providecommand{\tto}{\mathrel{\Rightarrow}} % Double arrow +\providecommand{\tfrom}{\mathrel{\Leftarrow}} % + +\providecommand{\mto}{\mapsto} + +\providecommand{\xto}[1]{\,\xrightarrow{#1}\,} +\providecommand{\xfrom}[1]{\,\xleftarrow{\;#1}\,} + +\providecommand{\To}{\mathrel{\Rightarrow}} % Double arrow +\providecommand{\From}{\mathrel{\Leftarrow}} + +\providecommand{\dar}{\kern-.75pt\operatorname{\downarrow}} +\providecommand{\uar}{\kern-.75pt\operatorname{\uparrow}} + +\providecommand{\Dar}{\kern-.75pt\operatorname{\Downarrow}} +\providecommand{\Uar}{\kern-.75pt\operatorname{\Uparrow}} + + +%% Logic +\providecommand{\True}{\top} +\providecommand{\False}{\bot} + +\providecommand{\bigor}{\bigvee} +\providecommand{\bigand}{\bigwedge} + +\providecommand{\impl}{\Rightarrow} +\providecommand{\equ}{\Longleftrightarrow} + +\providecommand{\entails}{\vdash} + +%% Order +\providecommand{\appr}{\sqsubseteq} +\providecommand{\join}{\sqcup} +\providecommand{\meet}{\sqcap} + +\providecommand{\bigjoin}{\bigsqcup} +\providecommand{\bigmeet}{\bigsqcap} + +%% Products +\providecommand{\fst}{\oname{fst}} +\providecommand{\snd}{\oname{snd}} +\providecommand{\pr}{\oname{pr}} + +\providecommand{\brks}[1]{\langle #1\rangle} +\providecommand{\Brks}[1]{\bigl\langle #1\bigr\rangle} + +%% Coproducts +\providecommand{\inl}{\oname{inl}} +\providecommand{\inr}{\oname{inr}} +\providecommand{\inj}{\oname{in}} + +\DeclareSymbolFont{Symbols}{OMS}{cmsy}{m}{n} +\DeclareMathSymbol{\iobj}{\mathord}{Symbols}{"3B} +%\DeclareRobustCommand{\iobj}{\emptyset} + +%% CCC +\providecommand{\curry}{\oname{curry}} +\providecommand{\uncurry}{\oname{uncurry}} +\providecommand{\ev}{\oname{ev}} + +% Semantic brackets +\RequirePackage{stmaryrd} + +\providecommand{\lsem}{\llbracket} +\providecommand{\rsem}{\rrbracket} +\providecommand{\sem}[1]{\lsem #1 \rsem} + +\providecommand{\Lsem}{\bigl\llbracket} +\providecommand{\Rsem}{\bigr\rrbracket} +\providecommand{\Sem}[1]{\Lsem #1 \Rsem} + +% Typographic +\providecommand{\comma}{,\operatorname{}\linebreak[1]} % possibly line-breaking comma +\providecommand{\dash}{\nobreakdash-\hspace{0pt}} % non-line-breaking hyphen +\providecommand{\erule}{\rule{0pt}{0pt}} % Empty object whose emptiness +% is not detected by LaTeX + +\providecommand{\by}[1]{\text{/\!\!/~#1}} % Comments in equations +\providecommand{\pacman}[1]{} % Hide a piece of text + +\newcommand{\undefine}[1]{\let #1\relax} % Make a command undefined + +\providecommand{\noqed}{\def\qed{}} % Undefine the QED symbol + +% -1 superscript for the inversion operator +\providecommand{\mone}{{\text{\kern.5pt\rmfamily-}\mathsf{\kern-.5pt1}}} + +\makeatletter +\@ifpackageloaded{enumitem}{}{ + \RequirePackage[loadonly]{enumitem} % without [loadonly] +} % conflicts with Beamer +\makeatother + +% Condensed list environments +\newlist{citemize}{itemize}{1} +\setlist[citemize]{label=\labelitemi,wide} +%leftmargin=0cm,itemindent=.7cm,labelwidth=\itemindent,labelsep=-.3cm,align=left} + +\newlist{cenumerate}{enumerate}{1} +\setlist[cenumerate,1]{label=\arabic*.~,ref={\arabic*},wide} +%leftmargin=0cm,itemindent=.7cm,labelwidth=\itemindent,labelsep=-.3cm,align=left} + +%\newenvironment{citemize}{\begin{itemize}[leftmargin=0cm,itemindent=.7cm,labelwidth=\itemindent,labelsep=-.3cm,align=left]}{\end{itemize}} +%\newenvironment{cenumerate}{\begin{enumerate}[leftmargin=0cm,itemindent=.7cm,labelwidth=\itemindent,labelsep=-.3cm,align=left]}{\end{enumerate}} + +%% A macro for defining mixfix operators +\makeatletter 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