Implication Details
Claim: If a category has finite products and is infinitary extensive, then it is infinitary 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 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 coproducts of Euclidean spaces
- category of Hausdorff spaces
- category of locally ringed spaces
- category of measurable spaces
- category of metric spaces with continuous maps
- category of metric spaces with ∞ allowed
- category of quivers with finite components
- category of schemes
- category of topological spaces
- category of Z-functors