I mean, I have something that reads
`\mathsf{Gr}(\varnothing)$. One can readily check $\mu$ is associative and unital with respect to $\eta$, so we have defined a monoid structure on $\mathsf{Gr}$.
In general, defining a monoid structure on a linear species $X$ corresponds to defining for each finite set and each decomposition $(S,T)$ of $I$ a map`