The Extensive Completion Of A Distributive Category (2001)
| Venue: | Theory Appl. Categ |
| Citations: | 7 - 1 self |
BibTeX
@ARTICLE{Cockett01theextensive,
author = {J.r.b. Cockett and Stephen Lack and D Ex /b},
title = {The Extensive Completion Of A Distributive Category},
journal = {Theory Appl. Categ},
year = {2001},
volume = {8},
pages = {8--541}
}
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Abstract
A category with finite products and finite coproducts is said to be distributive if the canonical map AB+AC # A (B +C) is invertible for all objects A, B, and C. Given a distributive category D , we describe a universal functor D # D ex preserving finite products and finite coproducts, for which D ex is extensive; that is, for all objects A and B the functor D ex /A D ex /B # D ex /(A + B) is an equivalence of categories. As an application, we show that a distributive category D has a full distributive embedding into the product of an extensive category with products and a distributive preorder. 1.
