Implication details
Claim: If a category is multi-cocomplete and has a terminal object, then it is cocomplete.
Proof: This follows from the dual implication.
This implication has a dual.
Show 26 categories using this implication
- category of finitely generated abelian groups
- category of finite abelian groups
- category of finite groups
- category of finite ordered sets
- category of finite sets
- category of finite-dimensional vector spaces
- category of finite-dimensional vector spaces [countable field]
- category of finite-dimensional vector spaces [finite field]
- category of finite-dimensional vector spaces [uncountable field]
- category of free abelian groups
- category of finitely generated free abelian groups
- category of countable groups
- category of smooth manifolds
- category of metric spaces with non-expansive maps
- category of metric spaces with continuous maps
- partially ordered set of natural numbers
- category of pseudo-metric spaces with non-expansive maps
- category of quivers with finite components
- category of schemes
- category of countable sets
- category of empty-or-finite pairs of sets
- category of combinatorial species
- category of countable-dimensional vector spaces
- category of finite Z-sets
- category of ω-sets
- walking splitting