Implication Details
Claim: If a category has countable powers and is essentially countable, then it is thin.
Proof: Adjust the proof of Mac Lane, V.2, Prop. 3.
Show 39 categories using this implication
- category of abelian groups
- category of abelian sheaves
- category of algebras
- category of Banach spaces with linear contractions
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of compact Hausdorff spaces
- category of filtered vector spaces
- category of finite-dimensional vector spaces [countable field]
- category of finitely generated abelian groups
- category of groups
- category of Jónsson-Tarski algebras
- category of left modules over a division ring
- category of left modules over a ring
- category of locally ringed spaces
- category of M-sets
- category of metric spaces with continuous maps
- category of metric spaces with ∞ allowed
- category of monoids
- category of pairs of sets
- category of partially ordered sets
- category of pointed sets
- category of preordered sets
- category of rings
- category of rngs
- category of semigroups
- category of set functions and commutative squares
- category of sets
- category of sets and relations
- category of sets with a distinguished subset
- category of sheaves
- category of simplicial sets
- category of small categories
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of vector spaces
- delooping of an infinite countable group
- delooping of the additive monoid of natural numbers