Implication details
Claim: If a category has countable coproducts and is extensive and is locally cartesian closed, then it is countably extensive.
Proof: The pullback functor preserves countable coproducts because it has a right adjoint.
This implication has a dual.
Show 15 categories using this implication
- trivial category
- category of F(I)-sets
- category of Jónsson-Tarski algebras
- category of M-sets
- category of quivers
- category of sequences of sets
- category of sets
- category of set functions and commutative squares
- category of large families of sets
- indiscrete category of sets
- category of pairs of sets
- category of sheaves
- category of Z-sets
- category of simplicial sets
- walking isomorphism