Implication details
Claim: If a category has powers, then it has ℵ₂-small powers.
Proof: This is trivial.
This implication has a dual.
Show 47 categories using this implication
- empty category
- discrete category on two objects
- delooping of the additive monoid of ordinal numbers
- 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 fields
- category of fields of characteristic zero
- category of free abelian groups
- category of countable groups
- category of finitely generated groups
- category of Jónsson-Tarski algebras
- category of M-sets
- category of smooth manifolds
- category of metric spaces with non-expansive maps
- category of metric spaces with continuous maps
- partially ordered set of natural numbers
- partially ordered collection of ordinal numbers
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets
- category of partially ordered sets without isolated points
- category of preordered sets
- category of quivers
- category of quivers with finite components
- category of schemes
- category of sequences of sets
- category of connected sequences of sets
- category of sets
- category of set functions and commutative squares
- category of sets and bijections
- category of countable sets
- discrete category of sets
- category of large families of sets and bijections
- category of large families of sets which are mostly empty
- category of sets with finite-to-one maps
- category of pairs of sets
- category of empty-or-finite pairs of sets
- category of sheaves
- category of countable-dimensional vector spaces
- category of large vector spaces over a large field with a small basis
- category of Z-sets
- preordered set of integers w.r.t. divisibility
- cocompletion of a discrete–pair join
- category of ω-sets
- category of simplicial sets
- walking span