  It is common to encounter symmetric monoidal categories $\mathcal{C}$ for
which every object is equipped with an algebraic structure, in a way that is
compatible with the monoidal product and unit in $\mathcal{C}$. We define this
formally and say that $\mathcal{C}$ supplies the algebraic structure. For
example, the category $\mathsf{Rel}$ of relations between sets has monoidal
structures given by both cartesian product and disjoint union, and with respect
to either one it supplies comonoids. We prove several facts about the notion of
supply, e.g. that the associators, unitors, and braiding of $\mathcal{C}$ are
automatically homomorphisms for any supply, as are the coherence isomorphisms
for any strong symmetric monoidal functor that preserve supplies. We also show
that any supply of structure in a symmetric monoidal category can be extended
to a supply of that structure on its strictification.
