Implication Details
Claim: If a category has coequalizers and has countable coproducts, then it has sequential colimits.
Proof: This follows from the dual implication.
Show 26 categories using this implication
- category of small categories
- category of cochain complexes of abelian groups
- category of compact Hausdorff spaces
- simplex category
- category of finite groups
- category of finite ordered sets
- category of free abelian groups
- category of countable groups
- category of Hausdorff spaces
- category of locally ringed spaces
- category of smooth manifolds
- category of measurable spaces
- category of metric spaces with continuous maps
- partially ordered set of extended natural numbers
- partially ordered collection of ordinal numbers
- category of partially ordered sets
- category of preordered sets
- category of schemes
- category of semigroups
- category of sequences of abelian groups
- category of pointed sets
- category of countable sets
- preordered set of integers w.r.t. divisibility
- category of graded abelian groups
- category of graded modules over a graded ring
- real interval [0,1]