Implication Details
Claim: If a category is cartesian closed and has finite coproducts, then it is distributive.
Proof: Each functor is left adjoint and hence preserves finite coproducts (in fact, all colimits).
Show 17 categories using this implication
- category of fields
- trivial category
- category of finite sets
- category of Jónsson-Tarski algebras
- category of M-sets
- partially ordered set of extended natural numbers
- category of sets
- category of set functions and commutative squares
- category of pairs of sets
- category of sheaves
- category of combinatorial species
- real interval [0,1]
- category of simplicial sets
- walking commutative square
- walking composable pair
- walking isomorphism
- walking morphism