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.
This implication has a dual.
Show 25 categories using this implication
- category of abelian groups
- category of finitely generated abelian groups
- category of cochain complexes of abelian groups
- category of finite abelian groups
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- 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 finitely generated free abelian groups
- category of finitely generated free modules over Z x Z
- category of finitely generated projective modules over the ring of dual numbers
- 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 empty-or-finite pairs of sets
- category of abelian sheaves
- category of vector spaces
- category of graded abelian groups
- category of graded modules over a graded ring
- walking span