Implication Details
Claim: If a category is one-way, then it has reflexive coequalizers.
Proof: Every reflexive pair is equal: If , then since (one-way), we must have , and likewise .
Show 10 categories using this implication
- category of free abelian groups
- category of metric spaces with continuous maps
- category of schemes
- category of sets and relations
- category of sets with finite-to-one maps
- category of smooth manifolds
- discrete category on two objects
- empty category
- partially ordered set of extended natural numbers
- trivial category