Implication details
Claim: If a category has pullbacks and is regular-quotient-trivial, then it has pullback-stable regular epimorphisms.
Proof: Regular epimorphisms are isomorphisms by assumption, and isomorphisms are clearly stable under pullback.
This implication has a dual.
Show 26 categories using this implication
- discrete category on two objects
- 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 Hausdorff spaces
- category of metric spaces with non-expansive maps
- category of metric spaces with continuous maps
- category of metric spaces with ∞ allowed
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets
- category of preordered sets
- category of schemes
- category of sets and bijections
- discrete category of sets
- category of large families of sets and bijections
- category of topological spaces
- category of pointed topological spaces
- category of uniform spaces
- preordered set of integers w.r.t. divisibility
- walking fork