Implication Details
Assumptions: finitely complete, right cancellative
Conclusions: regular subobject classifier
Reason: In a right cancellative category, every regular monomorphism is an isomorphism, so that a terminal object is a regular subobject classifier.
Show 17 categories using this implication
- trivial category
- category of Banach spaces with linear contractions
- category of commutative monoids
- category of compact Hausdorff spaces
- category of Hausdorff spaces
- category of metric spaces with continuous maps
- category of monoids
- poset of extended natural numbers
- category of posets
- category of rngs
- category of semigroups
- proset of integers w.r.t. divisibility
- poset [0,1]
- walking commutative square
- walking composable pair
- walking isomorphism
- walking morphism