Let $\mathcal{C}$ be an additive category, let $n \in \mathbb{N}$, and let $A_1,\ldots,A_n$ be objects of $\mathcal{C}$. Let $A$ be an object of $\mathcal{C}$ equipped with morphisms $\iota_i: A_i \to A$ and $\pi_i: A \to A_i$ for each $i \in \{1,\ldots,n\}$.
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For $i,j \in \{1,\ldots,n\}$, define the morphism $\delta_{ij}: A_j \to A_i$ by $\delta_{ij} = \operatorname{id}_{A_i}$ when $i=j$, and $\delta_{ij} = 0_{A_j,A_i}$ when $i \ne j$, where $0_{A_j,A_i}: A_j \to A_i$ is the zero morphism in $\mathcal{C}$.
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Then $(A,(\iota_i)_{i=1}^n,(\pi_i)_{i=1}^n)$ is a finite biproduct of $A_1,\ldots,A_n$ if and only if $(A,(\pi_i)_{i=1}^n)$ is a product of $A_1,\ldots,A_n$, $(A,(\iota_i)_{i=1}^n)$ is a coproduct of $A_1,\ldots,A_n$, and, for all $i,j \in \{1,\ldots,n\}$,