Implication Details
Claim: If a category has an initial object and is strongly connected and has a terminal object, then it is pointed.
Proof: By assumption there is a morphism . There is also a unique morphism . They are necessarily inverse to each other.
Show 13 categories using this implication
- simplex category
- category of filtered vector spaces
- category of finite ordered sets
- category of finite sets
- category of M-sets
- category of smooth manifolds
- category of metric spaces with non-expansive maps
- category of pseudo-metric spaces with non-expansive maps
- category of sets
- category of countable sets
- category of uniform spaces
- category of simplicial sets
- walking coreflexive pair