Implication details
Claim: If a category is Cauchy complete and is essentially small, then it is accessible.
Proof: See Makkai–Paré, Thm. 2.2.2.
This implication has a dual.
Show 24 categories using this implication
- empty category
- discrete category on two objects
- 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
- simplex category
- category of finite sets and injections
- category of finite abelian groups
- category of finite groups
- category of finite ordered sets
- category of finite sets
- category of countable groups
- category of finitely generated groups
- category of smooth manifolds
- partially ordered set of natural numbers
- category of countable sets
- category of countable-dimensional vector spaces
- category of finite Z-sets
- forked commutative square
- walking fork
- walking parallel pair
- walking span