Implication Details
Claim: If a category is countably extensive and has finite products, then it is countably distributive.
Proof: One can adjust the proof of Prop. 4.5 in Introduction to extensive and distributive categories by Carboni-Lack-Walters (which deals with the finite case).
This implication has a dual.
Show 18 categories using this implication
- category of sets with a binary relation
- category of small categories
- category of compact Hausdorff spaces
- category of Hausdorff spaces
- category of locally ringed spaces
- category of smooth manifolds
- category of measurable spaces
- category of metric spaces with continuous maps
- category of metric spaces with ∞ allowed
- category of partially ordered sets
- category of preordered sets
- category of schemes
- category of semigroups
- category of countable sets
- category of topological spaces
- category of uniform spaces
- category of Z-functors
- preordered set of integers w.r.t. divisibility