Distributive Category

A Category $\mathcal{C}$ with Finite Products and Finite Coproducts is distributive if the canonical map $(A\times X)+(A\times Y)\to A\times(X+Y)$ is an Isomorphism.

Properties

• A category $\mathcal{C}$ is distributive if and only if the Functor $A\times-:\mathcal{C}\to\mathcal{C}$ Preserves Finite Coproducts.
• Every distributive category has an Strict Initial Object.