\newcommand{\subsubsubsection}[1]{\textbf{#1}}
\newcommand{\WIP}{\textbf{WIP}}

\newcommand{\coloneqq}{\mathrel{\vcenter{\baselineskip0.5ex \lineskiplimit0pt
                     \hbox{\scriptsize.}\hbox{\scriptsize.}}}%
                     =}

\newcommand{\defeq}{\coloneqq}
\newcommand{\bN}{\mathbb{N}}
\newcommand{\bC}{\mathbb{C}}
\newcommand{\bX}{\mathbb{X}}
% \newcommand{\to}{\rightarrow}
\newcommand{\mto}{\mapsto}
\newcommand{\UU}{\ensuremath{\mathcal{U}}\xspace}
\let\type\UU
\newcommand{\MCU}{\UU}
\newcommand{\nomen}[1]{\emph{#1}}
\newcommand{\todo}[1]{\textit{#1}}
\newcommand{\comp}{\circ}
\newcommand{\x}{\times}
\newcommand\inv[1]{#1\raisebox{1.15ex}{$\scriptscriptstyle-\!1$}}
\newcommand{\tp}{\;\mathord{:}\;}
\newcommand{\Type}{\mathcal{U}}

\newcommand{\var}[1]{\mathit{#1}}
\newcommand{\Hom}{\mathit{Hom}}
\newcommand{\fmap}{\mathit{fmap}}
\newcommand{\idFun}{\mathit{id}}
\newcommand{\Sets}{\mathit{Sets}}
\newcommand{\Set}{\mathit{Set}}
\newcommand{\hSet}{\mathit{hSet}}
\newcommand{\id}{\mathit{id}}
\newcommand{\isEquiv}{\mathit{isEquiv}}
\newcommand{\idToIso}{\mathit{idToIso}}
\newcommand{\isSet}{\mathit{isSet}}
\newcommand{\isContr}{\mathit{isContr}}
\newcommand\Object{\mathit{Object}}
\newcommand\Functor{\mathit{Functor}}
\newcommand\isProp{\mathit{isProp}}
\newcommand\propPi{\mathit{propPi}}
\newcommand\propSig{\mathit{propSig}}
\newcommand\PreCategory{\mathit{PreCategory}}
\newcommand\IsPreCategory{\mathit{IsPreCategory}}
\newcommand\isIdentity{\mathit{isIdentity}}
\newcommand\propIsIdentity{\mathit{propIsIdentity}}
\newcommand\IsCategory{\mathit{IsCategory}}
\newcommand\Gl{\mathit{\lambda}}
\newcommand\lemPropF{\mathit{lemPropF}}
\newcommand\isPreCategory{\mathit{isPreCategory}}
\newcommand\congruence{\mathit{cong}}
\newcommand\identity{\mathit{identity}}
\newcommand\isequiv{\mathit{isequiv}}
\newcommand\qinv{\mathit{qinv}}
\newcommand\fiber{\mathit{fiber}}
\newcommand\shuffle{\mathit{shuffle}}
\newcommand\Univalent{\mathit{Univalent}}
\newcommand\refl{\mathit{refl}}
\newcommand\isoToId{\mathit{isoToId}}
\newcommand\rrr{\ggg}
\newcommand\fst{\mathit{fst}}
\newcommand\snd{\mathit{snd}}
\newcommand\Path{\mathit{Path}}
\newcommand\Category{\mathit{Category}}
\newcommand\TODO[1]{TODO: \emph{#1}}
\newcommand*{\QED}{\hfill\ensuremath{\square}}%
\newcommand\uexists{\exists!}
\newcommand\Arrow{\mathit{Arrow}}
