 Distributive category

In mathematics, a category is distributive if it has finite products and finite coproducts such that for every choice of objects formula_1, the canonical map

is an isomorphism, and for all objects formula_3, the canonical map formula_4 is an isomorphism (where 0 denotes the initial object).Equivalently, if for every object formula_3 the endofunctor formula_6 defined by formula_7 preserves coproducts up to isomorphisms formula_8.