Implication details
Claim: If a category is extensive and has quotients of congruences and is regular, then it has effective cocongruences.
Proof: This is proved as Corollary 5 here.
This implication has a dual.
Show 24 categories using this implication
- category of algebras
- 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 commutative monoids
- category of small categories
- category of compact Hausdorff spaces
- category of filtered vector spaces
- category of locally ringed spaces
- category of measurable spaces
- category of extended metric spaces
- category of monoids
- category of partially ordered sets
- category of preordered sets
- category of rings
- category of rngs
- category of semigroups
- category of countable sets
- category of topological spaces
- category of torsion-free abelian groups
- category of uniform spaces
- category of Z-functors
- category of ω-sets