Implication details
Claim: If a category is accessible, then it is Cauchy complete.
Proof: This is because the walking idempotent is -filtered for any regular cardinal . See also Makkai–Paré, Prop. 2.2.1.
This implication has a dual.
Show 29 categories using this implication
- category of finitely generated abelian groups
- category of coproducts of Euclidean spaces
- 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 finitely generated free modules over Z x Z
- category of Jónsson-Tarski algebras
- category of M-sets
- category of partially ordered sets without isolated points
- category of finitely generated projective modules over the ring of dual numbers
- category of quivers
- category of sets and relations
- category of sequences of sets
- category of sets
- category of set functions and commutative squares
- indiscrete category of sets
- category of pairs of sets
- category of sheaves
- category of abelian sheaves
- category of combinatorial species
- category of Z-sets
- real interval [0,1]
- category of simplicial sets
- walking idempotent
- walking isomorphism