The Extensive Completion of a Distributive Category
نویسنده
چکیده
A category with finite products and finite coproducts is said to be distributive if the canonical map A×B + A×C → A× (B + C) is invertible for all objects A, B, and C. Given a distributive category D , we describe a universal functor D → Dex preserving finite products and finite coproducts, for which Dex is extensive; that is, for all objects A and B the functor Dex/A × Dex/B → Dex/(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.
منابع مشابه
O ct 2 00 6 Restriction categories III : colimits , partial limits , and extensivity
A restriction category is an abstract formulation for a category of partial maps, defined in terms of certain specified idempotents called the restriction idempotents. All categories of partial maps are restriction categories; conversely, a restriction category is a category of partial maps if and only if the restriction idempotents split. Restriction categories facilitate reasoning about parti...
متن کاملA duality between fuzzy domains and strongly completely distributive $L$-ordered sets
The aim of this paper is to establish a fuzzy version of the dualitybetween domains and completely distributive lattices. All values aretaken in a fixed frame $L$. A definition of (strongly) completelydistributive $L$-ordered sets is introduced. The main result inthis paper is that the category of fuzzy domains is dually equivalentto the category of strongly completely distributive $L$-ordereds...
متن کاملA view on implementing processes : categories
We construct a category of circuits: the objects are alphabets and the morphisms are deterministic automata. The construction diiers in several respects from the bicategories of circuits appearing previously in the literature: it is parameterized by a monad which allows exibility in the emergent notion of process. We focus on the circuits which arise from a distributive category and the excepti...
متن کاملA Four for the Price of One Duality Principle for Distributive Spaces
In this paper we consider topological spaces as generalised orders and characterise those spaces which satisfy a (suitably defined) topological distributive law. Furthermore, we show that the category of these spaces is dually equivalent to a certain category of frames by simply observing that both sides represent the idempotents split completion of the same category.
متن کاملConnecting the profinite completion and the canonical extension using duality
We show using duality and category theory that the profinite completion  of a bounded distributive lattice expansion A is a homomorphic image of the canonical extension Aσ . Moreover the natural mapping μ : A →  can be extended to a surjection ν : Aσ ! Â.
متن کامل