Implication Details
Claim: If a category has disjoint finite coproducts and is regular-subobject-trivial, then it is trivial.
Proof: For any object , the unique morphism is a regular monomorphism, as the equalizer of the two coprojections . Therefore, it is an isomorphism.
Show 19 categories using this implication
- category of abelian groups
- category of abelian sheaves
- category of filtered vector spaces
- category of finite sets and bijections
- category of Jónsson-Tarski algebras
- category of left modules over a division ring
- category of left modules over a ring
- category of M-sets
- category of sets
- category of simplicial sets
- category of smooth manifolds
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of vector spaces
- delooping of a non-trivial finite group
- delooping of an infinite countable group
- delooping of an infinite uncountable group
- delooping of the additive monoid of natural numbers
- walking parallel pair