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.
This implication has a dual.
Show 36 categories using this implication
- delooping of the additive monoid of natural numbers
- category of Banach spaces with linear contractions
- category of sets equipped with a binary relation
- category of sets equipped with an irreflexive binary relation
- category of sets equipped with a symmetric binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- category of cochain complexes of abelian groups
- category of F(I)-sets
- 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 quivers
- category of quivers with finite components
- category of schemes
- category of sequences of abelian groups
- category of sequences of sets
- category of connected sequences of sets
- category of set functions and commutative squares
- category of sets and bijections
- category of pairs of sets
- category of empty-or-finite 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