Implication Details
Assumptions: additive
Conclusions: biproducts
Proof: This is standard, see e.g. Prop. 2.1 on the nLab.
Show 17 categories using this implication
- category of abelian groups
- category of abelian sheaves
- category of filtered vector spaces
- category of finite abelian groups
- 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 finitely generated abelian groups
- category of free abelian groups
- category of left modules over a division ring
- category of left modules over a ring
- category of rngs
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of vector spaces
- trivial category
- walking isomorphism