Implication details
Claim: If a category is locally copresentable and is locally presentable, then it is essentially small.
Proof: This follows from Adámek–Rosický, Thm. 1.64.
Show 39 categories using this implication
- category of abelian groups
- category of algebras
- category of Banach spaces with linear contractions
- category of sets equipped with a 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 reflexive binary relation
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of small categories
- category of cochain complexes of abelian groups
- category of compact Hausdorff spaces
- category of filtered vector spaces
- category of groups
- category of extended metric spaces
- category of monoids
- category of sets with a distinguished subset
- category of partially ordered sets
- category of preordered sets
- 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 rings
- category of rngs
- category of semigroups
- category of sequences of abelian groups
- category of sequences of sets
- category of pointed sets
- category of set functions and commutative squares
- category of pairs of sets
- category of sheaves
- category of abelian sheaves
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of vector spaces
- category of graded abelian groups
- category of graded modules over a graded ring