Implication details
Claim: If a category has pushouts and is regular-subobject-trivial, then it has pushout-stable regular monomorphisms.
Proof: This follows from the dual implication.
This implication has a dual.
Show 17 categories using this implication
- empty category
- 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
- category of finite sets and surjections
- category of groups
- category of countable groups
- category of finitely generated groups
- category of Hausdorff spaces
- category of sets and bijections
- discrete category of sets
- category of large families of sets and bijections
- preordered set of integers w.r.t. divisibility