Implication Details
Claim: If a category has disjoint finite coproducts and is locally cartesian closed, then it is extensive.
Proof: The pullback functor preserves finite coproducts because it has a right adjoint. Remark: In combination with other implication, this result implies that every elementary topos is extensive.
This implication has a dual.
Show 12 categories using this implication
- delooping of the additive monoid of ordinal numbers
- category of Banach spaces with linear contractions
- category of F(I)-sets
- category of finite sets
- category of finite sets of even cardinality
- category of groups
- category of monoids
- category of sets with a distinguished subset
- category of rngs
- category of large families of sets
- category of combinatorial species
- category of finite Z-sets