||This article may require cleanup to meet Wikipedia's quality standards. The specific problem is: there's more than one proposed notion under this name, see last ref in further reading (July 2014) (Learn how and when to remove this template message)|
is an isomorphism, and for all objects , the canonical map is an isomorphism. Equivalently. if for every object the functor 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.
- Cockett, J. R. B. (1993). "Introduction to distributive categories". Mathematical Structures in Computer Science. 3 (3): 277. doi:10.1017/S0960129500000232.
- Carboni, Aurelio (1993). "Introduction to extensive and distributive categories". Journal of Pure and Applied Algebra. 84 (2): 145–158. doi:10.1016/0022-4049(93)90035-R.
|This category theory-related article is a stub. You can help Wikipedia by expanding it.|