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% | |
% MAMA package (MAth MAcros) | |
% a semantic package for mathematical symbols and fast latexing | |
% | |
% by Matteo Capucci <matteo.capucci@gmail.com> | |
% | |
% comment on an equation | |
\newcommand{\comment}[1]{\qquad\text{#1}} | |
% overset without decreasing font size | |
\newcommand{\Overset}[2]{% | |
\mathop{#2}\limits^{\vbox to -.1ex{% | |
\kern -1.8ex\hbox{$#1$}\vss}}% | |
} | |
% underset without decreasing font size | |
\newcommand{\Underset}[2]{% | |
\mathop{#2}\limits_{\vbox to .1ex{% | |
\kern -.6ex\hbox{$#1$}\vss}}% | |
} | |
% hyphen for math mode | |
\mathchardef\dash="2D | |
% defined term | |
\newcommand{\defining}[1]{\textbf{#1}} | |
% subject of a thesis | |
\renewcommand{\th}[1]{\overset{th}{#1}} | |
% e costant | |
\newcommand{\e}{\mathrm{e}} | |
% exp | |
\renewcommand{\exp}{\operatorname{exp}} | |
% cotangent | |
\newcommand{\cotan}{\operatorname{cotan}} | |
% argmin | |
\newcommand{\argmin}{\operatorname{argmin}} | |
% 'does not imply' symbol | |
\newcommand{\nimplies}{\centernot\implies} | |
% implications in the opposite direction | |
\newcommand{\implied}{\Longleftarrow} | |
\newcommand{\nimplied}{\centernot\implied} | |
% logical implication | |
\newcommand{\limp}{\rightarrow} | |
\newcommand{\liff}{\leftrightarrow} | |
% inhabitation for types | |
\newcommand{\tin}{\!:\!} | |
% inverses of \to | |
\newcommand{\ot}{\leftarrow} | |
\newcommand{\from}{\ot} | |
% long version of \to | |
\newcommand{\longto}{\longrightarrow} | |
% inverse of \mapsto | |
% \newcommand{\mapsfrom}{\mathrel{\reflectbox{\ensuremath{\mapsto}}}} | |
% \newcommand{\longmapsfrom}{\mathrel{\reflectbox{\ensuremath{\longmapsto}}}} | |
% inclusion | |
\newcommand{\into}{\hookrightarrow} | |
\newcommand{\inot}{\hookleftarrow} | |
\newcommand{\mono}{\rightarrowtail} | |
% surjection | |
\newcommand{\onto}{\twoheadrightarrow} | |
\newcommand{\epi}{\twoheadrightarrow} | |
% iso arrows | |
\newcommand{\isoto}{\overset{\sim}\to} | |
\newcommand{\isolongto}{\overset{\sim}\longto} | |
% 2-morphisms | |
\newcommand{\twoto}{\Rightarrow} | |
\newcommand{\isotwoto}{\overset{\sim}\twoto} | |
\newcommand{\longtwoto}{\Longrightarrow} | |
\newcommand{\isolongtwoto}{\overset{\sim}\longtwoto} | |
% 3-morphisms | |
\newcommand{\threeto}{\Rrightarrow} | |
\newcommand{\narrow}[2]{\overset{#1}{#2}} | |
\newcommand{\nto}[1]{\narrow{#1}{\to}} | |
\newcommand{\nfrom}[1]{\narrow{#1}{\from}} | |
\newcommand{\nlongto}[1]{\xrightarrow{#1}} | |
\newcommand{\ninto}[1]{\narrow{#1}{\into}} | |
\newcommand{\nisoto}[1]{\narrow{#1}{\isolongto}} | |
\newcommand{\nepi}[1]{\narrow{#1}{\epi}} | |
\newcommand{\nmono}[1]{\narrow{#1}{\mono}} | |
% 'a | b' | |
\newcommand{\divides}{\,|\,} | |
% constant function | |
\newcommand{\cost}{\text{cost.}} | |
\newcommand{\const}{\mathsf{const}} | |
% locutions | |
\newcommand{\word}[1]{\quad\text{\underline{#1}}\quad} | |
\@ifpackagewith{babel}{italian}{% | |
\newcommand{\almosteverywhereon}[2][\mu]{{\text{${#1}$-q.o. su ${#2}$}}} | |
\renewcommand{\ae}{\ \text{q.o.}} | |
\newcommand{\sse}{\word{sse}} | |
\newcommand{\means}{\word{significa}} | |
\newcommand{\impl}{\word{implica}} | |
\newcommand{\fa}{\ \text{p.o.}\;} | |
}{% | |
\newcommand{\almosteverywhereon}[2][\mu]{{\text{${#1}$-a.e. on ${#2}$}}} | |
\renewcommand{\ae}{\ \text{a.e.}} | |
\newcommand{\sse}{\word{iff}} | |
\newcommand{\means}{\word{means}} | |
\newcommand{\impl}{\word{implies}} | |
\newcommand{\fa}{\ \text{f.a.}\;} | |
} | |
% such that | |
\newcommand{\suchthat}{\mid} | |
% numerical sets | |
\newcommand{\N}{\mathbb{N}} | |
\newcommand{\Z}{\mathbb{Z}} | |
\newcommand{\Q}{\mathbb{Q}} | |
\newcommand{\R}{\mathbb{R}} | |
%\newcommand{\C}{\mathbb{C}} | |
% set-theoretic stuff | |
\newcommand{\card}[1]{\left|{#1}\right|} | |
\newcommand{\parts}[1]{\mathcal{P}\left({#1}\right)} | |
\newcommand{\continuum}{\mathfrak{c}} | |
% diameter of a set | |
\newcommand{\diam}{\operatorname{diam}} | |
% vectors | |
\newcommand{\vers}[1]{\hat{\vv{#1}}} | |
\newcommand{\ii}{\vers{i}} | |
\newcommand{\jj}{\vers{j}} | |
\newcommand{\kk}{\vers{k}} | |
\newcommand{\xx}{\vv{x}} | |
\newcommand{\yy}{\vv{y}} | |
\newcommand{\zz}{\vv{z}} | |
% big kernel, cokernel & image | |
\newcommand{\Ker}{\operatorname{Ker}} | |
\newcommand{\coker}{\operatorname{coker}} | |
\newcommand{\Imm}{\operatorname{Im}} | |
\newcommand{\im}{\operatorname{im}} | |
% action of a group | |
\newcommand{\acts}{\curvearrowright} | |
% weak action groupoid | |
\newcommand{\wag}{\mathbin{/\mkern-6mu/}} | |
% direct sum | |
\newcommand{\dir}{\oplus} | |
\newcommand{\bigdir}{\bigoplus} | |
% operations in an Heyting algebra | |
\newcommand{\hey}{\Rightarrow} | |
\newcommand{\bigsup}{\bigvee} | |
\newcommand{\biginf}{\bigwedge} | |
% differential | |
\newcommand{\diff}[1]{\operatorname{d}{#1}} | |
% jacobian | |
\newcommand{\jac}{\operatorname{\vv{J}}} | |
% derivatives | |
\newcommand{\de}{\mathrm{d}} | |
\newcommand{\dx}{\de x} | |
\newcommand{\dt}{\de t} | |
\newcommand{\ds}{\de s} | |
\newcommand{\der}[2]{\frac{\de{#1}}{\de{#2}}} | |
\newcommand{\pder}[2]{\frac{\partial {#1}}{\partial {#2}}} | |
% second derivatives | |
\newcommand{\sder}[2]{\frac{\de^2{#1}}{\de{#2}^2}} | |
\newcommand{\spder}[3]{\frac{\partial^2{#1}}{\partial{#2} \partial{#3}}} | |
% second derivative on the same coordinate | |
\newcommand{\sdpder}[2]{\frac{\partial^2{#1}}{\partial{#2}^2}} | |
% big derivatives | |
\newcommand{\bigder}[2]{\dfrac{\strut \de{#1}}{\de{#2}}} | |
\newcommand{\bigpder}[2]{\dfrac{\strut \partial {#1}}{\partial {#2}}} | |
% big second derivatives | |
\newcommand{\bigsder}[2]{\dfrac{\strut \de^2 {#1}}{\de{#2}^2}} | |
\newcommand{\bigspder}[3]{\dfrac{\strut \partial^2 {#1}}{\partial {#2} \partial {#3}}} | |
% big second derivative on the same coordinate | |
\newcommand{\bigsdpder}[2]{\dfrac{\strut \partial^2 {#1}}{\partial {#2}^2}} | |
% left/right applied partial derivatives | |
\newcommand{\lpartial}{\overset{\leftarrow}\partial} | |
\newcommand{\rpartial}{\overset{\rightarrow}\partial} | |
% complex stuff | |
\newcommand{\conj}[1]{\overline{#1}} | |
\newcommand{\Arg}{\operatorname{Arg}} | |
\newcommand{\Res}{\operatorname{Res}} | |
% real and imaginary parts | |
\renewcommand{\Re}[1]{\mathfrak{Re}\left(#1\right)} | |
\renewcommand{\Im}[1]{\mathfrak{Im}\left(#1\right)} | |
% sign function | |
\newcommand{\sign}{\operatorname{}{sgn}} | |
% convergence | |
\newcommand{\conv}[1][]{\underset{{#1}}{\longrightarrow}} | |
% regularity classes | |
\newcommand{\Cn}{\mathcal{C}} | |
\newcommand{\Czero}{\Cn^0} | |
\newcommand{\Cone}{\Cn^1} | |
\newcommand{\Ctwo}{\Cn^2} | |
\newcommand{\Cinfty}{\Cn^\infty} | |
% Lipschitz | |
\newcommand{\Lip}{\mathrm{Lip}} | |
% indicator function | |
\newcommand{\ind}{\vv{1}} | |
% lenses | |
\newcommand{\lens}[2]{{#1 \choose #2}} | |
\renewcommand{\S}{\mathcal S} | |
\newcommand{\A}{\mathcal A} | |
\newcommand{\G}{\mathcal G} | |
\newcommand{\cat}[1]{\mathbf{#1}} | |
\newcommand{\dblcat}[1]{\cat{\mathbb #1}} | |
\newcommand{\trplcat}[1]{\cat{\mathfrak #1}} | |
\newcommand{\dblSet}{\dblcat{Set}} | |
\newcommand{\dblCat}{\dblcat{Cat}} | |
\newcommand{\Span}{\dblcat{Span}} | |
\newcommand{\DblCat}{\dblcat{DblCat}} | |
\newcommand{\DblIx}{\dblcat{Dbl}\dblcat{Ix}} | |
\newcommand{\MonDblIx}{\dblcat{Mon}\dblcat{Dbl}\dblcat{Ix}} | |
\newcommand{\Processes}{\dblcat{P}} | |
\newcommand{\CyberProcesses}{\trplcat{P}} | |
\newcommand{\Sys}{\cat{Sys}} | |
\newcommand{\Cyb}{\cat{Cyb}} | |
\newcommand{\CybSys}{\cat{CybSys}} | |
\newcommand{\Cont}{\cat{Cont}} | |
\newcommand{\doctrine}{\mathfrak{D}} | |
\newcommand{\theory}{\mathbb{T}} | |
\newcommand{\Theories}{\dblcat{Theories}} | |
\newcommand{\Behaviour}{\dblcat{Behav}} | |
\newcommand{\Obs}{\cat{Obs}} | |
\newcommand{\Org}{\dblcat{Org}} | |
\newcommand{\Poly}{\cat{Poly}} | |
\newcommand{\Moore}{\cat{Moore}} | |
\newcommand{\Games}{\cat{Games}} | |
\newcommand{\Players}{\cat{Plrs}} | |
\newcommand{\unilaxto}{\nlongto{\text{unitary lax}}} | |
\newcommand{\sys}[1]{\mathsf{#1}} | |
\newcommand{\dist}{\Delta} | |
\newcommand{\pow}{\mathcal{P}} | |
\newcommand{\cod}{\mathrm{cod}} | |
\newcommand{\dom}{\mathrm{dom}} | |
\newcommand{\st}{\mathrm{st}} | |
\newcommand{\nash}{\mathbf{n}} | |
\newcommand{\Sub}{\mathrm{Sub}} | |
\renewcommand{\H}{\mathcal H} | |
\newcommand{\K}{\mathcal K} | |
\newcommand{\U}{\mathcal U} | |
\renewcommand{\L}{\mathcal L} | |
\newcommand{\loss}{\ell}%{\mathsf{loss}} | |
\newcommand{\GD}{\mathsf{GD}} | |
\newcommand{\GF}{\mathsf{GF}} | |
\newcommand{\Comega}{{\mathchoice | |
{\rotatebox[origin=c]{180}{$\displaystyle \Omega$}}% \displaystyle | |
{\rotatebox[origin=c]{180}{$\textstyle \Omega$}}% \textstyle | |
{\rotatebox[origin=c]{180}{$\scriptstyle \Omega$}}% \scriptstyle | |
{\rotatebox[origin=c]{180}{$\scriptscriptstyle \Omega$}}% \scriptscriptstyle | |
}} | |
\DeclareMathOperator*{\Boxtimes}{\text{\raisebox{-0.25ex}{\scalebox{1.25}{$\boxtimes$}}}} | |
\newcommand{\Arenas}{\cat{Arenas}} | |
\newcommand{\Matrix}{\cat{Matrix}} | |
\newcommand{\fix}{\mathsf{fix}} | |
\renewcommand{\clock}{\text{\showclock{10}{10}}} | |
\newcommand{\Nature}{\mathcal N} | |
\newcommand{\eval}{\mathrm{eval}} | |
\newcommand{\curr}{\mathrm{curr}} | |
\newcommand{\true}{\mathsf{true}} | |
\newcommand{\view}{\mathsf{view}} | |
\newcommand{\play}{\mathsf{play}} | |
\newcommand{\coplay}{\mathsf{coplay}} | |
\newcommand{\expose}{\mathsf{expose}} | |
\newcommand{\update}{\mathsf{update}} | |
\renewcommand{\output}{\mathsf{output}} | |
\newcommand{\observe}{\mathsf{observe}} | |
\newcommand{\name}[1]{\lceil #1 \rceil} | |
\DeclareMathOperator{\argmax}{\mathrm{argmax}} | |
% identity | |
\newcommand{\identity}{\mathrm{id}} | |
\newcommand{\id}{\mathrm{id}} | |
% categories | |
\newcommand{\Ob}{\operatorname{Ob}} | |
\newcommand{\Hom}{\operatorname{Hom}} | |
\newcommand{\End}{\operatorname{End}} | |
\newcommand{\Aut}{\operatorname{Aut}} | |
\newcommand{\Nat}{\operatorname{Nat}} | |
% Kan extensions | |
\newcommand{\Lan}{\operatorname{Lan}} | |
\newcommand{\Ran}{\operatorname{Ran}} | |
% profunctor arrow | |
\newcommand{\profto}{\stackMath\mathrel{\stackinset{c}{-0.25ex}{c}{0.25ex}{\shortmid}{\to}}} | |
\newcommand{\longprofto}{\stackMath\mathrel{\stackinset{c}{-0.25ex}{c}{0.25ex}{\shortmid}{\longrightarrow}}} | |
\newcommand{\nprofto}[1]{\narrow{#1}{\profto}} | |
\newcommand{\horto}{\to} | |
\newcommand{\verto}{\stackMath\mathrel{\stackinset{c}{-0.25ex}{c}{0.25ex}{\bullet}{\to}}} | |
\newcommand{\longverto}{\stackMath\mathrel{\stackinset{c}{-0.25ex}{c}{0.25ex}{\bullet}{\longrightarrow}}} | |
\newcommand{\nhorto}[1]{\narrow{#1}{\horto}} | |
\newcommand{\nverto}[1]{\narrow{#1}{\verto}} | |
% big categories | |
\newcommand{\Cat}{\cat{Cat}} | |
\newcommand{\Prof}{\cat{Prof}} | |
\newcommand{\Set}{\cat{Set}} | |
\newcommand{\FinSet}{\cat{FinSet}} | |
\newcommand{\Mon}{\cat{Mon}} | |
\newcommand{\Grp}{\cat{Grp}} | |
\newcommand{\Mod}{\cat{Mod}} | |
\newcommand{\Ab}{\cat{Ab}} | |
\renewcommand{\Vec}{\cat{Vec}} | |
\newcommand{\Met}{\cat{Met}} | |
\newcommand{\Meas}{\cat{Meas}} | |
\newcommand{\Msbl}{\cat{Msbl}} | |
\newcommand{\Prob}{\cat{Prob}} | |
\newcommand{\Euc}{\cat{Euc}} | |
\newcommand{\Smooth}{\cat{Smooth}} | |
% opposite category | |
\newcommand{\op}{\mathsf{op}} | |
\newcommand{\co}{\mathsf{co}} | |
\newcommand{\coop}{\mathsf{coop}} | |
% isomorphism and equivalence symbols | |
\newcommand{\iso}[1][]{\overset{#1}{\cong}} | |
\newcommand{\equi}{\simeq} | |
% F left adjoint to G symbol | |
\newcommand{\adj}{\dashv} | |
\newcommand{\Para}{\cat{Para}} | |
\newcommand{\dblPara}{\dblcat{Para}} | |
\newcommand{\Proxy}{\cat{Proxy}} | |
\newcommand{\Copara}{\cat{Copara}} | |
\newcommand{\Optic}{\cat{Optic}} | |
\newcommand{\Lens}{\cat{Lens}} | |
\newcommand{\dblLens}{\dblcat{Lens}} | |
\newcommand{\DLens}{\cat{DLens}} | |
\newcommand{\DChart}{\cat{DChart}} | |
\newcommand{\Bun}{\mathrm{Bun}} | |
% monoidal products | |
\DeclareMathOperator{\extch}{\&} | |
\newcommand{\tensor}[1][\cat M]{\otimes_{#1}} | |
\newcommand{\mtimes}{\otimes} | |
\newcommand{\ntimes}{\oslash} | |
\newcommand{\ctimes}{\boxtimes} | |
\newcommand{\dtimes}{\boxdot} | |
\newcommand{\cplus}{\boxplus} | |
\newcommand{\copow}{\otimes} | |
% actions | |
\newcommand{\ostar}{\circledast} | |
\newcommand{\laction}{\smallblackdiamond} | |
\newcommand{\raction}{\diamond} | |
\newcommand{\waff}{\circledcirc} | |
\newcommand{\bothaction}{{\upperhalfcirc}} | |
\newcommand{\prodaction}{\bothaction^\times} | |
\newcommand{\coprodaction}{\bothaction^+} | |
\newcommand{\extchaction}{\bothaction^{\extch}} | |
% scaled & centered figures | |
\newcommand{\sctikzfig}[2][.8]{\begin{center}\scalebox{#1}{\tikzfig{#2}}\end{center}} | |
% fat semicolon | |
\newcommand{\comp}{\fatsemi} | |
% optic | |
\newcommand{\opticto}{\leftrightarrows} | |
\newcommand{\chartto}{\rightrightarrows} | |
\newcommand{\PsdMon}{\cat{PsdMon}} | |
\newcommand{\MonCat}{\twocat{M}\cat{onCat}} | |
\newcommand{\SymMonCat}{\twocat{S}\cat{ymMonCat}} | |
\newcommand{\BrMonCat}{\twocat{B}\cat{rMonCat}} | |
\newcommand{\Fib}{\twocat{F}\cat{ib}} | |
\newcommand{\OpFib}{\twocat{O}\cat{pFib}} | |
\newcommand{\deloop}{\twocat{B}} | |
\newcommand{\Kl}{\cat{Kl}} | |
\newcommand{\biKl}{\cat{biKl}} | |
\newcommand{\Alg}[1]{{#1}\dash\twocat{A}\cat{lg}} | |
\newcommand{\Bialg}[2]{({#1},{#2})\dash\twocat{B}\cat{iAlg}} | |
\newcommand{\lax}{\mathrm{lx}} | |
\newcommand{\oplax}{\mathrm{ox}} | |
\newcommand{\pseudo}{\mathrm{ps}} | |
\newcommand{\strict}{\mathrm{s}} | |
\newcommand{\braided}{\mathrm{br}} | |
\newcommand{\cart}{\mathrm{cart}} | |
\newcommand{\VCat}[1]{{#1}\dash\Cat} | |
\newcommand{\Actt}{\twocat{A}\cat{ct}} | |
\newcommand{\Act}[1]{{#1}\dash\Actt} | |
\newcommand{\Biactt}{\twocat{B}\cat{iact}} | |
\newcommand{\Biact}[2][\cat M]{{#1}\dash\Actt\dash{#2}} | |
\newcommand{\rev}{\mathrm{rev}} | |
\newcommand{\swap}{\mathrm{swap}} | |
\newcommand{\Bal}{\mathrm{Bal}} | |
\newcommand{\equalto}{=\mathrel{\mkern-3mu}=} | |
\newcommand{\Rho}{P} | |
\newcommand{\Alpha}{A} | |
\newcommand{\Day}{\mathrm{Day}} | |
\newcommand{\drinfeld}{\mathcal Z} | |
\newcommand{\Waff}{\cat W} | |
\makeatletter | |
\newcommand{\superimpose}[2]{% | |
{\ooalign{$#1\@firstoftwo#2$\cr\hfil$#1\@secondoftwo#2$\hfil\cr}}} | |
\makeatother | |
\newcommand{\revrel}[1]{\mathrel{\overset{\rev}{#1}}} | |
\newcommand{\colim}{\operatorname{colim}} | |
\newcommand{\rdev}{T^*} | |
\newcommand{\nopticto}[2]{\overset{#1}{\underset{#2}\opticto}} | |
\newcommand{\nchartto}[2]{\overset{#1}{\underset{#2}\chartto}} | |
\newcommand{\fflat}{{\flat\kern-1.4pt\flat}} | |
\newcommand{\hop}{\mathrm{hop}} | |
\newcommand{\vop}{\mathrm{vop}} | |
\newcommand{\trop}{\mathrm{top}} | |
\newcommand{\undertext}[2]{\underbrace{#1}_{\text{#2}}} |
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