macros.tex

%!TEX root = AnalyticStacks.tex

% \prism
\usepackage{relsize}
\usepackage[bbgreekl]{mathbbol}
\usepackage{amsfonts}
\DeclareSymbolFontAlphabet{\mathbb}{AMSb} % to ensure that the meaning of \mathbb does not change
\DeclareSymbolFontAlphabet{\mathbbl}{bbold}
\newcommand{\prism}{{\mathlarger{\mathbbl{\Delta}}}} 
% random bits of notation

\newcommand{\<}{\langle}
\let\>=\undefined
\newcommand{\>}{\rangle}

\newcommand{\ul}{\underline}
\newcommand{\citeme}{\textcolor{red}{cite me}}
\newcommand{\lf}{\left\lfloor}
\newcommand{\rf}{\right\rfloor}
\newcommand{\lc}{\left\lceil}
\newcommand{\rc}{\right\rceil}

\newcommand{\resp}{\quad\text{resp.}\quad}

% power series ring
\newcommand{\psr}[1]{[\![#1]\!]}

% Laurent series ring
\newcommand{\lsr}[1]{(\!(#1)\!)}

\newcommand{\actson}{\curvearrowright}
\newcommand{\actedonby}{\curvearrowleft}
\newcommand{\shift}{\mathrm{shift}}
\newcommand{\st}{\mid}

\newcommand{\ds}{\displaystyle}

\newcommand{\id}{\mathrm{id}}

\newcommand{\op}{\mathrm{op}}

\newcommand{\defeq}{\mathrel{:=}}
\newcommand{\eqdef}{\mathrel{=:}}
\newcommand{\tops}{\texorpdfstring}

\DeclareMathOperator{\ev}{ev}

\DeclareMathOperator{\res}{res}
\DeclareMathOperator{\tr}{tr}

% fancy diagram shortcuts
\newdir{ >}{{}*!/-10pt/@{>}}
\newcommand{\pullback}{\ar@{}[dr]|<<{\mbox{\Huge$\lrcorner$}}}
\newcommand{\pushout}{\ar@<2pt>@{}[ul]|<{\mbox{\Huge$\ulcorner$}}}

% symbols
\newcommand{\A}{\mathbf A}
\newcommand{\C}{\mathbf C}
\newcommand{\cF}{\mathcal F}
\newcommand{\sF}{\mathscr F}
\newcommand{\F}{\mathbf F}
\newcommand{\G}{\mathbf G}
\renewcommand{\H}{\mathrm H}
\DeclareMathOperator{\K}{K}
\renewcommand{\L}{\mathbf L}
\newcommand{\M}{\mathcal M}
\newcommand{\N}{\mathbf N}
\renewcommand{\O}{\mathcal O}
\renewcommand{\P}{\mathbf P}
\newcommand{\cP}{\mathcal P}
\newcommand{\Q}{\mathbf Q}
\newcommand{\R}{\mathbf R}
\let\sec=\S
\renewcommand{\S}{\mathbf S}
\newcommand{\T}{\mathbf T}
\newcommand{\W}{\mathbf W}
\newcommand{\Z}{\mathbf Z}
\newcommand{\bdry}{\partial}

\newcommand{\RP}{\mathbf{RP}}
\newcommand{\CP}{\mathbf{CP}}

\newcommand{\Fil}{\mathsf{F}}
\newcommand{\Nyg}{\mathcal{N}}

\newcommand{\tnsr}{\otimes}

\newcommand{\morph}{\mathop{\longrightarrow}\limits}
\newcommand{\xra}{\xrightarrow}

\newcommand{\from}{\mathop{\leftarrow}}

\renewcommand{\lim}{\mathop{\operatorname*{lim}\limits_{\longleftarrow}}\limits}
\newcommand{\colim}{\mathop{\operatorname*{lim}\limits_{\longrightarrow}}\limits}

% arrows
\newcommand{\epi}{\twoheadrightarrow}
\newcommand{\mono}{\hookrightarrow}
\newcommand{\monic}{\mathop{\rightarrowtail}\limits}
\newcommand{\iso}{\overset\sim\longrightarrow}
\newcommand{\eqv}{\simeq}
\newcommand{\isom}{\cong}

\newcommand{\Ainf}{{\mathbf{A}_{\mathrm{inf}}}}
\newcommand{\BK}{{\mathfrak S}}
\newcommand{\WCart}{\mathrm{WCart}}

%Theorem Styles
\newtheorem{theorem}{Theorem}[section]
\newtheorem*{theorem*}{Theorem}

\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{proposition}[theorem]{Proposition}

\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{desiderata}[theorem]{Desiderata}
\newtheorem{example}[theorem]{Example}
\newtheorem{goal}[theorem]{Goal}
\newtheorem{idea}[theorem]{Idea}
\newtheorem{question}[theorem]{Question}
\newtheorem{remark}[theorem]{Remark}
\newtheorem*{sketch}{Proof sketch}
\newtheorem*{answer}{Answer}
\newtheorem{warning}[theorem]{Warning}

\renewcommand{\~}{\widetilde}
\renewcommand{\^}{\widehat}
\newcommand{\can}{\mathrm{can}}

\newcommand{\note}[1]{\textcolor{purple}{#1}}

\newcommand{\gasopen}{\Z[\hat q^\pm]^\gas}

% operators
\DeclareMathOperator{\AnSpec}{AnSpec}
\DeclareMathOperator{\Aut}{Aut}
\DeclareMathOperator{\End}{End}
\DeclareMathOperator{\Ext}{Ext}
\DeclareMathOperator{\Fin}{Fin}
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\Hom}{Hom}
\DeclareMathOperator{\Lie}{Lie}
\DeclareMathOperator{\Mod}{Mod}
\DeclareMathOperator{\PGL}{PGL}
\DeclareMathOperator{\Psh}{Psh}
\DeclareMathOperator{\Pro}{Pro}
\DeclareMathOperator{\QCoh}{QCoh}
\DeclareMathOperator{\RHom}{RHom}
\DeclareMathOperator{\fib}{fib}
\DeclareMathOperator{\Sh}{Sh}
\DeclareMathOperator{\Spa}{Spa}
\DeclareMathOperator{\Spec}{Spec}
\DeclareMathOperator{\Spf}{Spf}
\DeclareMathOperator{\Tor}{Tor}

\DeclareMathOperator{\lcm}{lcm}
\DeclareMathOperator{\coker}{coker}

% categories
\newcommand{\Ab}{\mathrm{Ab}}
\newcommand{\An}{\mathrm{An}}
\newcommand{\AnRing}{\mathrm{AnRing}}
\newcommand{\CRing}{\mathrm{CRing}}
\newcommand{\Cat}{\mathrm{Cat}}
\newcommand{\Cond}{\mathrm{Cond}}
\newcommand{\Set}{\mathrm{Set}}
\newcommand{\Solid}{\mathrm{Solid}}
\newcommand{\Sp}{\mathrm{Sp}}

% stacks
\newcommand{\Vect}{\text{Vect}}

\newcommand{\Aff}{\text{Aff}}
\newcommand{\Betti}{\text{Betti}}
\newcommand{\an}{\mathrm{an}}
\newcommand{\dR}{\mathrm{dR}}
\newcommand{\fpqc}{\mathrm{fpqc}}
\newcommand{\gas}{\mathrm{gas}}
\newcommand{\gq}{\mathbin{\!/\!\!/\!}}
\newcommand{\liq}{\mathrm{liq}}
\newcommand{\qgas}{\text{$q$-gas}}
\newcommand{\solid}{\blacksquare}
\newcommand{\tri}{\triangleright}


\newcommand{\size}{\mathrm{size}}
\newcommand{\weight}{\mathrm{weight}}
\newcommand{\Zar}{\text{Zar}}
\newcommand{\et}{\text{\'et}}

% project macros

% YouTube link - defined in each article
\newcommand{\yt}[2]{}

% change to generate completed pdf

\newif\ifcompleted
\completedfalse

\ifcompleted
  \excludecomment{unfinished}
\else
  \newenvironment{unfinished}[1]{
    \color{BrickRed}\textbf{Unfinished starting from #1}

  }{\color{black}}
\fi

% unfinished section
\newcommand{\ufs}{\tops{\color{BrickRed}}{}}