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.
This implication has a dual.
Show 55 categories using this implication
- empty category
- trivial category
- discrete category on two objects
- category of large families of abelian groups
- category of sets equipped with a binary relation
- category of sets equipped with an irreflexive binary relation
- category of sets equipped with a reflexive binary relation
- category of sets equipped with a symmetric binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- category of sets equipped with a symmetric reflexive binary relation
- category of small categories
- category of cochain complexes of abelian groups
- category of compact Hausdorff spaces
- category of filtered vector spaces
- category of countable groups
- category of Hausdorff spaces
- category of Jónsson-Tarski algebras
- category of locally ringed spaces
- category of M-sets
- category of measurable spaces
- category of extended metric spaces
- category of sets with a distinguished subset
- partially ordered set of extended natural numbers
- partially ordered collection of ordinal numbers
- category of partially ordered sets
- category of preordered sets
- category of quivers
- category of semigroups
- category of sequences of abelian groups
- category of sequences of sets
- category of sets
- category of set functions and commutative squares
- category of countable sets
- category of large families of sets which are mostly empty
- indiscrete category of sets
- category of pairs of sets
- category of sheaves
- category of topological spaces
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of long transfinite sequences of abelian groups
- category of uniform spaces
- category of large families of vector spaces which are mostly zero
- category of large vector spaces over a large field with a small basis
- category of Z-functors
- category of Z-sets
- category of graded abelian groups
- category of graded modules over a graded ring
- real interval [0,1]
- category of simplicial sets
- walking commutative square
- walking composable pair
- walking isomorphism
- walking morphism
- walking span