Implication details
Claim: If a category has countable products and has equalizers, then it is ℵ₁-cofiltered.
Proof: This follows from the dual implication.
This implication has a dual.
Show 25 categories using this implication
- category of large families of abelian groups
- category of sets equipped with a 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 reflexive binary relation
- category of cochain complexes of abelian groups
- category of compact Hausdorff spaces
- category of F(I)-sets
- category of filtered vector spaces
- category of Hausdorff spaces
- category of locally ringed spaces
- category of measurable spaces
- category of metric spaces with continuous maps
- category of sets with a distinguished subset
- category of sequences of abelian groups
- category of large families of sets
- category of large families of sets which are mostly singletons
- 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 large families of vector spaces which are mostly zero
- category of Z-functors
- category of graded abelian groups
- category of graded modules over a graded ring