Definition:Additive Category
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Definition
Let $A$ be a preadditive category.
Definition 1: binary biproducts
The category $A$ is an additive category if and only if:
- it has a zero object
- it has all binary biproducts.
Definition 2: binary products
The category $A$ is an additive category if and only if:
- it has a zero object
- it has all binary products.
Definition 3: binary coproducts
The category $A$ is an additive category if and only if:
- it has a zero object
- it has all binary coproducts.
Definition 4: finite biproducts
The category $A$ is an additive category if and only if it has all finite biproducts.
Definition 5: finite products
The category $A$ is an additive category if and only if it has all finite products.
Definition 6: finite coproducts
The category $A$ is an additive category if and only if 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
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