Implication Details
Claim: If a category has finite coproducts and is strongly connected, then it has disjoint finite coproducts.
Proof: This follows from the dual implication.
Show 31 categories using this implication
- category of abelian groups
- category of finitely generated abelian groups
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- category of Banach spaces with linear contractions
- category of commutative monoids
- category of cochain complexes of abelian groups
- category of filtered vector spaces
- 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 groups
- category of countable groups
- category of monoids
- 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 sets and relations
- category of rngs
- category of sequences of abelian groups
- category of pointed sets
- category of abelian sheaves
- category of pointed topological spaces
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of vector spaces
- category of graded abelian groups
- category of graded modules over a graded ring