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).
Show 12 categories using this implication
- category of abelian sheaves
- category of compact Hausdorff spaces
- category of sets and relations
- category of sets with a distinguished subset
- category of simplicial sets
- partially ordered set of extended natural numbers
- partially ordered set of natural numbers
- preordered set of integers w.r.t. divisibility
- real interval [0,1]
- walking commutative square
- walking composable pair
- walking span