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.
This implication has a dual.
Show 31 categories using this implication
- category of abelian groups
- category of finite sets and bijections
- delooping of a group
- delooping of an infinite countable group
- delooping of an infinite uncountable group
- delooping of the additive monoid of natural numbers
- category of cochain complexes of abelian groups
- category of filtered vector spaces
- category of finite sets of even cardinality
- category of finitely generated free modules over Z x Z
- category of Jónsson-Tarski algebras
- category of M-sets
- category of finitely generated projective modules over the ring of dual numbers
- category of left modules over a ring
- category of left modules over a division ring
- category of left modules over a non-semisimple ring
- category of sequences of abelian groups
- category of sets
- category of sets and bijections
- category of large families of sets and bijections
- category of abelian sheaves
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of vector spaces
- category of large vector spaces over a large field with a small basis
- category of Z-sets
- forked commutative square
- category of graded abelian groups
- category of graded modules over a graded ring
- category of simplicial sets
- walking parallel pair