Implication details
Claim: If a category has an extremal generating collection, then it has a generating collection.
Proof: This is trivial.
This implication has a dual.
Show 42 categories using this implication
- empty category
- trivial category
- discrete category on two objects
- category of finite sets and bijections
- category of Banach spaces with linear contractions
- category of cochain complexes of abelian groups
- category of F(I)-sets
- category of finite sets and surjections
- category of finite abelian groups
- category of finite groups
- category of fields
- category of fields of characteristic zero
- category of locally ringed spaces
- partially ordered set of extended natural numbers
- 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 large families of sets
- category of large families of sets and bijections
- category of large families of sets which are mostly empty
- category of large families of sets which are mostly singletons
- category of pairs of sets
- category of empty-or-finite pairs of sets
- category of sheaves
- category of combinatorial species
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of large families of vector spaces which are mostly zero
- category of Z-functors
- category of finite Z-sets
- cocompletion of a discrete–pair join
- category of graded abelian groups
- category of graded modules over a graded ring
- real interval [0,1]
- walking commutative square
- walking composable pair
- walking isomorphism