Definition:Additive Category

Definition
Let $A$ be a preadditive category.

Definition 1: binary biproducts
The category $A$ is an additive category :
 * it has a zero object
 * it has all binary biproducts.

Definition 2: binary products
The category $A$ is an additive category :
 * it has a zero object
 * it has all binary products.

Definition 3: binary coproducts
The category $A$ is an additive category :
 * it has a zero object
 * it has all binary coproducts.

Definition 4: finite biproducts
The category $A$ is an additive category it has all finite biproducts.

Definition 5: finite products
The category $A$ is an additive category it has all finite products.

Definition 6: finite coproducts
The category $A$ is an additive category it has all finite coproducts.

Also see

 * Equivalence of Definitions of Additive Category
 * Definition:Abelian Category
 * Finite Product in Preadditive Category is Biproduct
 * Finite Coproduct in Preadditive Category is Biproduct