Implication details
Claim: If a category is balanced and has a generator, then it has an extremal generator.
Proof: This is immediate from the fact that any faithful functor out of a balanced category is also conservative (see here).
This implication has a dual.
Show 21 categories using this implication
- category of large families of abelian groups
- 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 compact Hausdorff spaces
- category of sets with a distinguished subset
- partially ordered set of natural numbers
- partially ordered set of extended natural numbers
- category of sets and relations
- category of abelian sheaves
- category of long transfinite sequences of abelian groups
- category of countable-dimensional vector spaces
- category of large vector spaces over a large field with a small basis
- preordered set of integers w.r.t. divisibility
- forked commutative square
- real interval [0,1]
- category of simplicial sets
- walking commutative square
- walking composable pair
- walking span