Implication Details
Claim: If a category is accessible, then it has an extremal generating collection.
Proof: The collection appearing in the definition of a -accessible category gives an essentially small dense full subcategory, which is in particular an extremal generating collection.
Show 27 categories using this implication
- delooping of the additive monoid of natural numbers
- category of Banach spaces with linear contractions
- category of sets with a binary relation
- category of cochain complexes of abelian groups
- category of directed graphs
- category of filtered vector spaces
- category of fields
- category of fields of characteristic zero
- category of Hausdorff spaces
- category of locally ringed spaces
- category of measurable spaces
- category of sets with a distinguished subset
- category of schemes
- category of sequences of abelian groups
- category of set functions and commutative squares
- category of pairs of sets
- category of sheaves
- category of abelian sheaves
- category of topological spaces
- category of pointed topological spaces
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of uniform spaces
- category of large families of vector spaces which are mostly zero
- category of graded abelian groups
- category of graded modules over a graded ring
- category of simplicial sets