In mathematics, a category is distributive if it has finite products and finite coproducts such that for every choice of objects
is an isomorphism, and for all objects
In particular, if the functor
For example, Set is distributive, while Grp is not, even though it has both products and coproducts.
An even simpler category that has both products and coproducts but is not distributive is the category of pointed sets.