Implication Details
Claim: If a category has coequalizers of kernel pairs and has effective congruences, then it has quotients of congruences.
Proof: Every congruence is a kernel pair, thus has a coequalizer.
Show 15 categories using this implication
- category of algebras
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of groups
- category of monoids
- category of rings
- category of rngs
- category of semigroups
- category of set functions and commutative squares
- category of pairs of sets
- category of simplicial sets
- walking commutative square
- walking composable pair
- walking morphism