Implication details
Claim: If a category is cototal, then it is complete.
Proof: This follows from the dual implication.
This implication has a dual.
Show 46 categories using this implication
- empty category
- discrete category on two objects
- category of finitely generated abelian groups
- category of finite sets and bijections
- delooping of a group
- delooping of an infinite countable group
- delooping of a non-trivial finite group
- delooping of an infinite uncountable group
- delooping of the additive monoid of natural numbers
- simplex category
- category of coproducts of Euclidean spaces
- category of finite groups
- category of finite ordered sets
- category of finite sets
- 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 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 fields
- category of finitely generated free abelian groups
- category of finitely generated free modules over Z x Z
- category of countable groups
- category of finitely generated groups
- category of metric spaces with non-expansive maps
- partially ordered collection of ordinal numbers
- category of pseudo-metric spaces with non-expansive maps
- 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 connected sequences of sets
- category of sets and bijections
- discrete category of sets
- category of large families of sets which are mostly empty
- category of non-empty sets
- category of combinatorial species
- category of large vector spaces over a large field with a small basis
- cocompletion of a discrete–pair join
- forked commutative square
- category of ω-sets
- walking coreflexive pair
- walking idempotent
- walking parallel pair
- walking splitting