Implication Details
Claim: If a category is finitely complete and is right cancellative, then it has a regular subobject classifier.
Proof: In a right cancellative category, every regular monomorphism is an isomorphism, so that a terminal object is a regular subobject classifier.
Show 18 categories using this implication
- trivial category
- category of Banach spaces with linear contractions
- category of commutative monoids
- category of small categories
- category of compact Hausdorff spaces
- category of Hausdorff spaces
- category of metric spaces with continuous maps
- category of monoids
- partially ordered set of extended natural numbers
- category of partially ordered sets
- category of semigroups
- category of abelian sheaves
- preordered set of integers w.r.t. divisibility
- real interval [0,1]
- walking commutative square
- walking composable pair
- walking isomorphism
- walking morphism