Our work is a fundamental study of the notion of approximation inQ-categories and in (U,Q)-categories. Our exposition is categorical but kept as close to language of domain theory as possible. Consequently, we introduce auxiliary, approximating and Scott-continuous distributors, the way-below distributor, and continuity of Qand (U,Q)-categories. We fully characterize J-continuous Q-categories (...

background: gastric lavage (gl) is one of the most commonly used decontamination method for cholinergic insecticide ingestion in developing countries despite lack of supporting evidence. this study was designed to evaluate the outcome of patients with cholinergic insecticide poisoning treated with gl in regards to timing and frequency of the procedure. methods: in this prospective observational...

Based on the notion of $Q$-sup-lattices (a fuzzy counterpart of complete join-semilattices valuated in a commutative quantale), we present the concept of $Q$-sup-algebras -- $Q$-sup-lattices endowed with a collection of finitary operations compatible with the fuzzy joins. Similarly to the crisp case investigated in cite{zhang-laan}, we characterize their subalgebras and quotients, and following...

A main purpose of this paper is to explain how the theory of higher spin fields in flat D = 4 space and in AdS4 emerges as a result of the quantization of a superparticle propagating in so called tensorial superspaces which have the property of a ‘generalized conformal’ or simply General Linear (GL) flatness.

A 2-form between two sup-lattices L and R is defined to be a suplattice bimorphism L×R → 2. Such 2-forms are equivalent to Galois connections, and we study them and their relation to quantales, involutive quantales and quantale modules. As examples we describe applications to C*-algebras.

It is observed that the axioms for partial metrics with values in quantales coincide with the axioms for Q-sets (M -valued sets, sets with fuzzy equality, quantale-valued sets) for commutative quantales. Ω-sets correspond to the case of partial ultrametrics.

We show that for a commutative quantale V every functor Set −→ V -cat has an enriched leftKan extension. As a consequence, coalgebras over Set are subsumed by coalgebras over V -cat. Moreover, one can build functors on V -cat by equipping Set-functors with a metric. 1998 ACM Subject Classification F.4.1 Mathematical Logic

If the standard concepts of partial-order relation and subset are fuzzified, taking valuation in a unital commutative quantale Q, corresponding concepts of joins and join-preserving mappings can be introduced. We present constructions of limits, colimits and Hom-objects in categories Q-Sup of Q-valued fuzzy joinsemilattices, showing the analogy to the ordinary category Sup of join-semilattices.