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).
This implication has a dual.
Show 28 categories using this implication
- category of fields
- trivial category
- category of F(I)-sets
- category of finite sets
- category of finite-dimensional vector spaces
- category of finite-dimensional vector spaces [countable field]
- category of finite-dimensional vector spaces [finite field]
- category of finite-dimensional vector spaces [uncountable field]
- category of Jónsson-Tarski algebras
- category of M-sets
- partially ordered set of extended natural numbers
- 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 combinatorial species
- category of finite Z-sets
- category of Z-sets
- real interval [0,1]
- category of simplicial sets
- walking commutative square
- walking composable pair
- walking isomorphism
- walking morphism