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.
This implication has a dual.
Show 20 categories using this implication
- category of algebras
- category of sets equipped with an irreflexive binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of finite sets of cardinality a power of 3
- category of monoids
- category of quivers
- category of quivers with finite components
- category of rings
- category of rngs
- category of semigroups
- category of sequences of sets
- category of set functions and commutative squares
- category of pairs of sets
- category of simplicial sets
- walking commutative square
- walking composable pair
- walking morphism