A New Approach to Quantitative Domain Theory

This paper introduces a new approach to the theory of Ω-categories enriched by a frame. The approach combines ideas from various areas such as generalized ultrametric domains, Ω-categories, constructive analysis, and fuzzy mathematics. As the basic framework, we use the Wagner’s Ω-category [18,19] with a frame instead of a quantale with unit. The objects and morphisms in the category will be called L-Fuzzy posets and L-Fuzzy monotone mappings, respectively. Moreover, we introduce concepts of adjoints and a kind of convergence in an L-Fuzzy poset that makes the theory “constructive” or “computable”.