Implication details
Claim: If a category is finitely accessible, then it is ℵ₁-accessible.
Proof: This is because any regular cardinal is strictly smaller than its successor cardinal. See nLab.
This implication has a dual.
Show 50 categories using this implication
- empty category
- trivial category
- discrete category on two objects
- category of large families of abelian groups
- 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
- 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 coproducts of Euclidean spaces
- category of F(I)-sets
- category of finite sets and surjections
- category of filtered vector 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 free abelian groups
- category of finitely generated free modules over Z x Z
- category of finitely generated groups
- category of measurable spaces
- category of metric spaces with continuous maps
- category of partially ordered sets without isolated points
- category of sets and relations
- category of connected sequences of sets
- category of sets and bijections
- discrete category of sets
- category of large families of sets
- category of large families of sets and bijections
- category of large families of sets which are mostly singletons
- category of non-empty sets
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of long transfinite sequences of abelian groups
- category of uniform spaces
- category of large families of vector spaces which are mostly zero
- category of Z-functors
- cocompletion of a discrete–pair join
- forked commutative square
- category of ω-sets
- walking fork
- walking idempotent
- walking isomorphism
- walking parallel pair