Implication details
Claim: If a category is cototal, then it is cocomplete.
Proof: This follows from the dual implication.
This implication has a dual.
Show 20 categories using this implication
- category of sets equipped with an irreflexive binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- category of finite sets and injections
- category of finite sets and surjections
- category of finite abelian groups
- category of fields of characteristic zero
- category of free abelian groups
- category of smooth manifolds
- category of metric spaces with continuous maps
- partially ordered set of natural numbers
- category of quivers with finite components
- category of schemes
- category of countable sets
- category of large families of sets which are mostly singletons
- category of sets with finite-to-one maps
- category of empty-or-finite pairs of sets
- category of countable-dimensional vector spaces
- category of finite Z-sets
- walking fork
- walking span