Implication Details
Claim: If a category is extensive and has finite products, then it is distributive.
Proof: This is Prop. 4.5 in Introduction to extensive and distributive categories by Carboni-Lack-Walters.
This implication has a dual.
Show 14 categories using this implication
- category of sets equipped with a binary relation
- category of sets equipped with a reflexive binary relation
- category of sets equipped with a symmetric binary relation
- category of sets equipped with a symmetric reflexive binary relation
- category of compact Hausdorff spaces
- category of Hausdorff spaces
- category of locally ringed spaces
- category of measurable spaces
- category of sets with a distinguished subset
- category of schemes
- category of countable sets
- category of topological spaces
- category of uniform spaces
- category of Z-functors