\section{Rigs}
\subsection{definition}
\subsection{augmentated rigs}
For our purpose of applying rieg theory to enumerative combinatorics, it is natural to consider homomorphism from a ri(e)g to $\N$. We call such a structure, augmentation. \memo{It's conventional in ring theory}
\begin{definition}
    For a rig $R$, an ($\N$-)augmentation of $R$ is a rig homomorphism $R\to \N$.
\end{definition}