About: Distributive category

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In mathematics, a category is distributive if it has finite products and finite coproducts and such that for every choice of objects , the canonical map is an isomorphism, and for all objects , the canonical map is an isomorphism (where 0 denotes the initial object). Equivalently, if for every object the endofunctor defined by preserves coproducts up to isomorphisms . It follows that and aforementioned canonical maps are equal for each choice of objects.

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  • In mathematics, a category is distributive if it has finite products and finite coproducts and such that for every choice of objects , the canonical map is an isomorphism, and for all objects , the canonical map is an isomorphism (where 0 denotes the initial object). Equivalently, if for every object the endofunctor defined by preserves coproducts up to isomorphisms . It follows that and aforementioned canonical maps are equal for each choice of objects. In particular, if the functor has a right adjoint (i.e., if the category is cartesian closed), it necessarily preserves all colimits, and thus any cartesian closed category with finite coproducts (i.e., any bicartesian closed category) is distributive. (en)
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  • July 2014 (en)
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  • there's more than one proposed notion under this name, see last ref in further reading (en)
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  • In mathematics, a category is distributive if it has finite products and finite coproducts and such that for every choice of objects , the canonical map is an isomorphism, and for all objects , the canonical map is an isomorphism (where 0 denotes the initial object). Equivalently, if for every object the endofunctor defined by preserves coproducts up to isomorphisms . It follows that and aforementioned canonical maps are equal for each choice of objects. (en)
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  • Distributive category (en)
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