Implication details
Claim: A category is locally finitely multi-presentable if and only if it is finitely accessible and is multi-cocomplete.
Proof: This follows from one of the equivalent formulations of locally finitely multi-presentable categories.
Show 20 categories using this implication
- empty category
- discrete category on two objects
- category of sets equipped with an irreflexive binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- category of small categories
- category of coproducts of Euclidean spaces
- category of finite sets and surjections
- 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 finitely generated free modules over Z x Z
- category of partially ordered sets
- category of partially ordered sets without isolated points
- category of preordered sets
- category of sets and relations
- discrete category of sets
- category of empty-or-finite pairs of sets
- category of large vector spaces over a large field with a small basis
- walking idempotent
- walking splitting