Implication details
Claim: If a category is cocomplete and is an elementary cotopos, then it is complete.
Proof: This follows from the dual implication.
This implication has a dual.
Show 12 categories using this implication
- category of coproducts of Euclidean spaces
- category of free abelian groups
- category of countable groups
- category of smooth manifolds
- category of metric spaces with continuous maps
- category of quivers with finite components
- category of schemes
- category of countable sets
- category of non-empty sets
- category of countable-dimensional vector spaces
- category of large vector spaces over a large field with a small basis
- cocompletion of a discrete–pair join