Recall that a bijection is both surjective and injective.
There is a prop Bij where morphisms are bijections
\(m\ne n \implies\) ?\(\mathbf{Bij}(m,n)=\varnothing)\)
Bij is a ?subcategory of \(\ref{FinSet as prop|\textbf{FinSet|referenced}}\), so we can use the same monoidal product.