Implication Details
Claim: If a category has an extremal cogenerating collection, then it has a cogenerating collection.
Proof: This follows from the dual implication.
This implication has a dual.
Show 38 categories using this implication
- empty category
- discrete category on two objects
- category of finitely generated abelian groups
- category of algebras
- category of finite sets and bijections
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of small categories
- category of finite sets and injections
- category of finite abelian groups
- category of finite groups
- category of finite-dimensional vector spaces
- category of finite-dimensional vector spaces [countable field]
- category of finite-dimensional vector spaces [finite field]
- category of finite-dimensional vector spaces [uncountable field]
- category of fields
- category of fields of characteristic zero
- category of groups
- category of countable groups
- category of Hausdorff spaces
- category of monoids
- partially ordered set of extended natural numbers
- category of finitely generated projective modules over the ring of dual numbers
- category of rings
- category of rngs
- category of semigroups
- category of large families of sets which are mostly empty
- category of large families of sets which are mostly singletons
- category of sets with finite-to-one maps
- category of torsion-free abelian groups
- category of long transfinite sequences of abelian groups
- category of large families of vector spaces which are mostly zero
- cocompletion of a discrete–pair join
- real interval [0,1]
- walking commutative square
- walking composable pair
- walking morphism