Implication details
Claim: If a category has a quotient object classifier, then it is epi-regular and is finitely cocomplete.
Proof: This follows from the dual implication.
This implication has a dual.
Show 71 categories using this implication
- empty category
- discrete category on two objects
- 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 equipped with a binary relation
- category of sets equipped with an irreflexive 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 irreflexive binary relation
- category of sets equipped with a symmetric reflexive binary relation
- category of small categories
- simplex category
- category of coproducts of Euclidean spaces
- category of finite sets and surjections
- category of filtered vector spaces
- category of finite groups
- category of finite sets of even cardinality
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- category of fields
- category of free abelian groups
- category of finitely generated free abelian groups
- category of finitely generated free modules over Z x Z
- category of finitely generated 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 extended metric spaces
- 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 finitely generated projective modules over the ring of dual numbers
- category of quivers with finite components
- category of schemes
- category of semigroups
- category of connected sequences of sets
- category of sets and bijections
- discrete category of sets
- category of large families of sets and bijections
- category of large families of sets which are mostly singletons
- category of sets with finite-to-one maps
- category of non-empty sets
- category of empty-or-finite pairs of sets
- category of topological spaces
- category of torsion-free abelian groups
- category of uniform spaces
- preordered set of integers w.r.t. divisibility
- forked commutative square
- category of ω-sets
- real interval [0,1]
- walking commutative square
- walking composable pair
- walking coreflexive pair
- walking fork
- walking idempotent
- walking parallel pair
- walking span
- walking splitting