Combinatorialists refer to a functor $F\colon \textup{\textsf{cat}}{\mathrm{iso}} \to \textup{\textsf{cat}}$ as a species. The image $F(n)$ of the $n$-element set $n$ is the set of labeled $F$-structures on $n$. The set of unlabeled $F$-structures on $n$ is defined by restricting $\textup{\textsf{cat}}{\mathrm{iso}}$ to the full subcategory spanned by the $n$-element set, i.e., to the symmetric group $\Sigma_n$ regarded as the group of automorphisms of the object $n \in \textup{\textsf{cat}}_{\mathrm{iso}}$, and forming the colimit of the diagram \(\mathsf{B}\Sigma_n \hookrightarrow \textup{\textsf{cat}}_{\mathrm{iso}} \xrightarrow{F} \textup{\textsf{cat}}.\) Because $\textup{fun}$ and $\textup{fun}$ are objectwise isomorphic, the sets of labeled $\textup{fun}$-structures and labeled $\textup{fun}$-structures are isomorphic. However, the set of unlabeled $\textup{fun}$-structures on $n$ is the set of conjugacy classes of permutations of $n$-elements, while the set of unlabeled $\textup{fun}$-structures on $n$ is trivial: all linear orders on $n$ are isomorphic. See \cite{joyal-species} for more.