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-Pare, Prop. 2.2.1.
Show 17 categories using this implication
- category of abelian sheaves
- category of Banach spaces with linear contractions
- category of finite-dimensional vector spaces [countable field]
- category of finite-dimensional vector spaces [uncountable field]
- category of Jónsson-Tarski algebras
- category of M-sets
- category of metric spaces with ∞ allowed
- category of non-empty sets
- category of pairs of sets
- category of set functions and commutative squares
- category of sets
- category of sets and relations
- category of sheaves
- category of simplicial sets
- real interval [0,1]
- walking idempotent
- walking isomorphism