Direct sum universal property

Direct sum universal property: Let $\{M_i\}_{i\in I}$ be a family of $R$-modules, and let $\iota_i:M_i\to \bigoplus_{i\in I}M_i$ be the canonical maps. For any $R$-module $N$ and any family of homomorphisms $f_i:M_i\to N$, there exists a unique homomorphism $f:\bigoplus_{i\in I}M_i\to N$ such that $f\circ \iota_i=f_i$ for all $i\in I$.

This is the defining coproduct property of the direct sum in the category of $R$-modules, stated in terms of module homomorphisms .