Implication Details
Claim: If a category has coequalizers and has countable coproducts, then it is ℵ₁-filtered.
Proof: Every countable diagram even admits a universal cocone.
Show 32 categories using this implication
- category of abelian sheaves
- category of compact Hausdorff spaces
- category of countable groups
- category of countable sets
- category of filtered vector spaces
- category of Hausdorff spaces
- category of Jónsson-Tarski algebras
- category of locally ringed spaces
- category of M-sets
- category of measurable spaces
- category of pairs of sets
- category of semigroups
- category of set functions and commutative squares
- category of sets
- category of sets with a distinguished subset
- category of sheaves
- category of simplicial sets
- category of topological spaces
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of Z-functors
- discrete category on two objects
- empty category
- partially ordered collection of ordinal numbers
- partially ordered set of extended natural numbers
- real interval [0,1]
- trivial category
- walking commutative square
- walking composable pair
- walking isomorphism
- walking morphism
- walking span