Implication details
Claim: If a category is one-way, then it has reflexive coequalizers.
Proof: The two morphisms of every reflexive pair are equal: If , then since the category is one-way, so we must have , and likewise .
This implication has a dual.
Show 13 categories using this implication
- empty category
- trivial category
- discrete category on two objects
- category of sets equipped with an irreflexive binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- category of free abelian groups
- category of smooth manifolds
- category of metric spaces with continuous maps
- partially ordered set of extended natural numbers
- category of quivers with finite components
- category of schemes
- discrete category of sets
- category of sets with finite-to-one maps