Distributivity Over Coproducts. We have isomorphisms of sets
\begin{align*} \delta ^{\mathsf{Sets}}_{\ell } & \colon A\times \webleft (B\mathchoice {\mathbin {\textstyle \coprod }}{\mathbin {\textstyle \coprod }}{\mathbin {\scriptstyle \textstyle \coprod }}{\mathbin {\scriptscriptstyle \textstyle \coprod }}C\webright ) \overset {\scriptstyle \mathord {\sim }}{\dashrightarrow }\webleft (A\times B\webright )\mathchoice {\mathbin {\textstyle \coprod }}{\mathbin {\textstyle \coprod }}{\mathbin {\scriptstyle \textstyle \coprod }}{\mathbin {\scriptscriptstyle \textstyle \coprod }}\webleft (A\times C\webright ),\\ \delta ^{\mathsf{Sets}}_{r} & \colon \webleft (A\mathchoice {\mathbin {\textstyle \coprod }}{\mathbin {\textstyle \coprod }}{\mathbin {\scriptstyle \textstyle \coprod }}{\mathbin {\scriptscriptstyle \textstyle \coprod }}B\webright )\times C \overset {\scriptstyle \mathord {\sim }}{\dashrightarrow }\webleft (A\times C\webright )\mathchoice {\mathbin {\textstyle \coprod }}{\mathbin {\textstyle \coprod }}{\mathbin {\scriptstyle \textstyle \coprod }}{\mathbin {\scriptscriptstyle \textstyle \coprod }}\webleft (B\times C\webright ), \end{align*}
natural in $A,B,C\in \text{Obj}\webleft (\mathsf{Sets}\webright )$.