Implication Details
Claim: If a category is cartesian closed and has coproducts, then it is infinitary distributive.
Proof: Each functor is left adjoint and hence preserves coproducts (in fact, all colimits).
This implication has a dual.
Show 26 categories using this implication
- trivial category
- category of small categories
- category of F(I)-sets
- category of finite sets
- category of Jónsson-Tarski algebras
- category of M-sets
- category of measurable spaces
- partially ordered set of extended natural numbers
- category of partially ordered sets
- category of preordered 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
- category of large families of sets which are mostly singletons
- indiscrete category of sets
- category of pairs of sets
- category of sheaves
- category of Z-sets
- real interval [0,1]
- category of simplicial sets
- walking commutative square
- walking composable pair
- walking isomorphism
- walking morphism