[[Category theory MOC]]
# Additive category

An **additive category** is a [[category]] which is [[Enriched category|enriched]] over [[Category of abelian groups]] and admits finite [[Biproduct|biproducts]], #m/def/cat 
thus

- [[Products and coproducts]] agree in a canonical way;
- A [[zero object]] exists; and
- Hom-sets are [[Abelian group|abelian groups]] and composition is [[Multilinear map|bilinear]].

A stronger notion is a [[Preäbelian category]].

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