Implication Details
Claim: If a category has reflexive coequalizers, then it has quotients of congruences.
Proof: A congruence has a common section given by the reflexivity morphism.
This implication has a dual.
Show 69 categories using this implication
- empty category
- trivial category
- discrete category on two objects
- category of large families of abelian groups
- category of finite sets and bijections
- delooping of a group
- delooping of an infinite countable group
- delooping of a non-trivial finite group
- delooping of an infinite uncountable group
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- category of sets with a binary relation
- category of small categories
- category of cochain complexes of abelian groups
- category of coproducts of Euclidean spaces
- category of finite sets and injections
- category of finite sets and surjections
- category of finite sets
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- category of fields
- category of fields of characteristic zero
- category of finitely generated free abelian groups
- category of groups
- category of Hausdorff spaces
- category of locally ringed spaces
- category of smooth manifolds
- category of measurable spaces
- category of metric spaces with non-expansive maps
- category of metric spaces with continuous maps
- category of metric spaces with ∞ allowed
- category of sets with a distinguished subset
- partially ordered set of natural numbers
- partially ordered set of extended natural numbers
- partially ordered collection of ordinal numbers
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets
- category of partially ordered sets without isolated points
- category of preordered sets
- category of schemes
- category of sequences of abelian groups
- category of pointed sets
- discrete category of sets
- category of large families of sets
- category of large families of sets which are mostly empty
- category of large families of sets which are mostly singletons
- category of non-empty sets
- category of sheaves
- category of combinatorial species
- category of topological spaces
- category of pointed topological spaces
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of long transfinite sequences of abelian groups
- category of uniform spaces
- category of large families of vector spaces which are mostly zero
- category of large vector spaces over a large field with a small basis
- preordered set of integers w.r.t. divisibility
- cocompletion of a discrete–pair join
- forked commutative square
- category of graded abelian groups
- category of graded modules over a graded ring
- real interval [0,1]
- walking coreflexive pair
- walking fork
- walking idempotent
- walking parallel pair
- walking span
- walking splitting