Implication Details
Claim: If a category is Cauchy complete and is essentially finite, then it has cofiltered limits and has cofiltered-limit-stable epimorphisms.
Proof: This follows from the dual implication.
This implication has a dual.
Show 53 categories using this implication
- empty category
- discrete category on two objects
- category of abelian groups
- category of algebras
- delooping of the additive monoid of ordinal numbers
- category of sets equipped with a binary relation
- category of sets equipped with an irreflexive binary relation
- category of sets equipped with a reflexive binary relation
- category of sets equipped with a symmetric binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- category of sets equipped with a symmetric reflexive binary relation
- category of commutative algebras
- category of commutative rings
- category of small categories
- category of cochain complexes of abelian groups
- category of finite sets and surjections
- category of filtered vector spaces
- category of groups
- category of locally ringed spaces
- category of smooth manifolds
- category of measurable spaces
- category of monoids
- category of sets with a distinguished subset
- category of partially ordered sets
- category of preordered sets
- category of left modules over a ring
- category of left modules over a division ring
- category of left modules over a non-semisimple ring
- category of rings
- category of rngs
- category of semigroups
- category of sequences of abelian groups
- category of pointed sets
- category of countable sets
- category of large families of sets which are mostly empty
- category of large families of sets which are mostly singletons
- category of topological spaces
- category of pointed topological spaces
- category of torsion-free abelian groups
- category of uniform spaces
- category of vector spaces
- category of countable-dimensional vector spaces
- category of Z-functors
- cocompletion of a discrete–pair join
- forked commutative square
- category of graded abelian groups
- category of graded modules over a graded ring
- walking commutative square
- walking coreflexive pair
- walking fork
- walking parallel pair
- walking span
- walking splitting