Implication Details
Claim: If a category has disjoint finite coproducts and is regular-quotient-trivial, then it is trivial.
Proof: For any object , the coequalizer of the two coprojections is the codiagonal . Therefore, these two coprojections are equal. But their equalizer is also the unique morphism . It follows that is an isomorphism.
Show 25 categories using this implication
- category of abelian groups
- category of abelian sheaves
- category of Banach spaces with linear contractions
- category of countable sets
- category of filtered vector spaces
- category of finite abelian groups
- category of finite sets and injections
- category of finitely generated abelian groups
- category of free abelian groups
- 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 metric spaces with continuous maps
- category of schemes
- category of sets
- category of sets and relations
- category of sets with a distinguished subset
- category of sets with finite-to-one maps
- category of simplicial sets
- category of smooth manifolds
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of vector spaces
- walking fork