Distributive category

In mathematics, a category is distributive if it has finite products and finite coproducts such that for every choice of objects ${\displaystyle A,B,C}$, the canonical map

is an isomorphism, and for all objects ${\displaystyle A}$, the canonical map ${\displaystyle 0\to A\times 0}$ is an isomorphism. Equivalently. if for every object ${\displaystyle A}$ the functor ${\displaystyle A\times -}$ preserves coproducts up to isomorphisms ${\displaystyle f}$. It follows that ${\displaystyle f}$ and aforementioned canonical maps are equal for each choice of objects.

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