Implication Details
Claim: If a category is locally copresentable and is locally presentable, then it is essentially small.
Proof: This follows from Adamek-Rosicky, Thm. 1.64.
Show 32 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 groups
- category of Jónsson-Tarski algebras
- category of left modules over a division ring
- category of left modules over a ring
- category of M-sets
- 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 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