In this paper we study interpretations and equivalences of propositional deductive systems by using a quantale-theoretic approach introduced by Galatos and Tsinakis. Our aim is to provide a general order-theoretic framework which is able to describe and characterize both strong and weak forms of interpretations among propositional deductive systems also in the cases where the systems have diffe...

We explain the precise relationship between two module-theoretic descriptions of sheaves on an involutive quantale, namely the description via so-called Hilbert structures on modules and that via so-called principally generated modules. For a principally generated module satisfying a suitable symmetry condition we observe the existence of a canonical Hilbert structure. We prove that, when worki...

In this work, we describe an adjunction between the comma category of Set-based monads under the V -powerset monad and the category of associative lax extensions of Set-based monads to the category of V -relations. In the process, we give a general construction of the Kleisli extension of a monad to the category of V-relations.

We prove in this paper that for a quasi-compact and semiseparated (non necessarily noetherian) scheme X, the derived category of quasi-coherent sheaves over X, D(Aqc(X)), is a stable homotopy category in the sense of Hovey, Palmieri and Strickland, answering a question posed by Strickland. Moreover we show that it is unital and algebraic. We also prove that for a noetherian semi-separated forma...

This document contains a rough summary of the main theorems discussed during the mini-course on Baker-Beynon Duality for unital latticeordered Abelian groups and MV-algebras held at Bowling Green State University from 8.VI.2009 through 12.VI.2009, with references to the original sources. Bibliographic Note. The standard reference on MV-algebras is [10]. It develops all of the basic theory in ca...

Abstract It is proved that the class of c-closed distribution spaces contains extremal domains and codomains to make convolution distributions a well-defined bilinear mapping. The are systematically endowed with topologies bornologies hypocontinuous whenever defined. Largest modules smallest algebras for semigroups constructed along same lines. fact exist within this fundamentally related quant...

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...

In the topos approach to quantum theory of Doering and Isham the Kochen–Specker Theorem, which asserts the contextual nature of quantum theory, can be reformulated in terms of the global sections of a presheaf characterised by the Gelfand spectrum of a commutativeC∗–algebra. In previous work we showed how this topos perspective can be generalised to a class of categories typically studied withi...

We say that a class D of categories is the Bourn localization of a class C of categories, and we write D = Loc(C), if D is the class of all (finitely complete) categories D such that for each object A in D, Pt(D ↓ A) ∈ C, where Pt(D ↓ A) denotes the category of all pointed objects in the comma-category (D ↓ A). As D.Bourn showed, if we take D to be the class of Mal’tsev categories in the sense ...

In this paper, we take a GL-quantale as the truth value table to study a new rough set model—L-valued fuzzy rough sets. The three key components of this model are: an L-fuzzy set A as the universal set, an L-valued relation of A and an L-fuzzy set of A (a fuzzy subset of fuzzy sets). Then L-valued fuzzy rough sets are completely characterized via both constructive and axiomatic approaches.