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\section{Introduction}\label{SectionIntroduction}
\subsection{Motivation 0: Riegs themselves}
\cite{599172}
\subsection{Motivation 1: Topoi}
\subsubsection{Burnside-type rig}
\subsubsection{Atomic quotients}
\cite{yoshida1987burnside}
\memo{Liouville's divisor theorem}
\subsection{Motivation 2: Logic, Equational theory}
Tarski's high school problem, \cite{fiore2006remarks}
\cite{gurevivc1985equational}
\cite{GUREVIC19901} \memo{Decidability of equational consequences of HSI (?)}



\cite{henry2017localic}
\subsection{Motivation 3: Combinatorics}
\subsection{Motivation 4: Modular arithmetic with exponentials}
\subsection{Motivation 5: Rig theory}
\cite{gondran2008graphs}
\subsection{Motivation 6: As a Heyting algebra with quantity}