Implication details
Claim: If a category is a generalized variety, then it is ℵ₁-accessible.
Proof: See Adámek–Rosický, Rem. 4.8(2).Remark: A generalized variety is not necessarily finitely accessible, see Kawase.
Show 64 categories using this implication
- category of abelian groups
- category of large families of abelian groups
- category of algebras
- delooping of the additive monoid of ordinal numbers
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of cochain complexes of abelian groups
- category of F(I)-sets
- category of finite sets of even cardinality
- category of finite sets of odd cardinality
- category of fields
- category of fields of characteristic zero
- category of free abelian groups
- category of finitely generated free modules over Z x Z
- category of groups
- category of finitely generated groups
- category of Jónsson-Tarski algebras
- category of M-sets
- category of measurable spaces
- category of metric spaces with continuous maps
- category of monoids
- partially ordered set of extended natural numbers
- category of quivers
- 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 sets and relations
- category of rings
- category of rngs
- category of semigroups
- category of sequences of abelian groups
- category of sequences of sets
- category of sets
- category of pointed sets
- category of set functions and commutative squares
- 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
- indiscrete category of sets
- category of pairs of sets
- category of topological spaces
- category of long transfinite sequences of abelian groups
- category of uniform spaces
- category of vector spaces
- category of large families of vector spaces which are mostly zero
- category of large vector spaces over a large field with a small basis
- category of Z-functors
- category of Z-sets
- cocompletion of a discrete–pair join
- category of graded abelian groups
- category of graded modules over a graded ring
- category of ω-sets
- category of simplicial sets
- walking commutative square
- walking composable pair
- walking coreflexive pair
- walking idempotent
- walking morphism
- walking splitting
- dual of the category of sets
- dual of the category of topological spaces