Implication Details
Claim: A category is additive if and only if it has finite coproducts and is preadditive.
Proof: This follows from the dual implication.
Show 21 categories using this implication
- category of abelian groups
- category of finitely generated abelian groups
- category of cochain complexes of abelian groups
- simplex category
- category of finite abelian groups
- category of finite-dimensional vector spaces
- category of finite-dimensional vector spaces [countable field]
- category of finite-dimensional vector spaces [finite field]
- category of finite-dimensional vector spaces [uncountable field]
- category of free abelian groups
- category of left modules over a ring
- category of left modules over a division ring
- category of left modules over a non-semisimple ring
- category of sequences of abelian groups
- category of non-empty sets
- category of abelian sheaves
- category of vector spaces
- category of graded abelian groups
- category of graded modules over a graded ring
- walking coreflexive pair
- walking span