Implication Details
Claim: If a category has coequalizers and is finitely complete and is locally cartesian closed, then it is regular.
Proof: See Johnstone, Lemma A1.5.13. From this it follows also that every elementary topos is regular.
This implication has a dual.
Show 19 categories using this implication
- 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 small categories
- category of F(I)-sets
- category of finite sets
- category of Hausdorff spaces
- category of measurable spaces
- category of sets with a distinguished subset
- category of partially ordered sets
- category of preordered sets
- category of large families of sets
- category of large families of sets which are mostly singletons
- category of sheaves
- category of combinatorial species
- category of topological spaces
- category of pointed topological spaces
- category of finite Z-sets