Implication Details
Claim: If a category is balanced and has a generating collection, then it has an extremal generating collection.
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 8 categories using this implication
- category of large families of abelian groups
- category of compact Hausdorff spaces
- category of Hausdorff spaces
- category of measurable spaces
- category of sets and relations
- category of pointed topological spaces
- category of long transfinite sequences of abelian groups
- category of large vector spaces over a large field with a small basis