Implication Details
Claim: If a category has effective congruences and is regular, then it has quotients of congruences.
Proof: We assume that every congruence is effective, and the regularity condition implies that every effective congruence has a quotient.
Show 25 categories using this implication
- category of algebras
- category of Banach spaces with linear contractions
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of compact Hausdorff spaces
- category of finite groups
- category of groups
- category of countable groups
- category of Jónsson-Tarski algebras
- category of M-sets
- category of monoids
- category of rings
- category of rngs
- category of semigroups
- category of sets
- category of set functions and commutative squares
- category of countable sets
- category of pairs of sets
- category of Z-functors
- category of simplicial sets
- walking commutative square
- walking composable pair
- walking isomorphism
- walking morphism