Implication Details
Claim: If a category is subobject-trivial, then it has coreflexive equalizers and has reflexive coequalizers.
Proof: Any parallel pair of morphisms with a common section (or retraction) must be a pair of equal isomorphisms.
Show 13 categories using this implication
- simplex category
- category of coproducts of Euclidean spaces
- category of finite sets of even cardinality
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- category of smooth manifolds
- category of partially ordered sets without isolated points
- category of finitely generated projective modules over the ring of dual numbers
- category of sets and relations
- category of sets with finite-to-one maps
- category of non-empty sets
- walking coreflexive pair
- walking idempotent