Implication Details
Claim: If a category has kernel pairs and has quotients of congruences, then it has coequalizers of kernel pairs.
Proof: This is simply because a kernel pair is a congruence.
This implication has a dual.
Show 46 categories using this implication
- empty 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 small categories
- category of finite sets and injections
- category of finite sets of even cardinality
- category of finite sets of odd cardinality
- category of fields
- category of fields of characteristic zero
- category of finitely generated free modules over Z x Z
- category of Hausdorff spaces
- category of locally ringed spaces
- 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
- partially ordered set of natural numbers
- partially ordered collection of ordinal numbers
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets
- category of preordered sets
- category of sets and relations
- category of schemes
- 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 empty
- category of sets with finite-to-one maps
- category of non-empty sets
- category of topological spaces
- category of pointed topological spaces
- category of torsion abelian groups
- category of long transfinite sequences of abelian groups
- category of uniform spaces
- forked commutative square
- walking fork
- walking idempotent
- walking parallel pair
- walking span