For a completely distributive quantale L, L-fuzzy strongest postcondition predicate transformers are introduced, and it is shown that, under reasonable assumptions, they are linear or affine continuous mappings between continuous L-idempotent semimodules of L-fuzzy monotonic predicates. © 2012 Elsevier B.V. All rights reserved.

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.

In this paper, we study the category of quantale-valued preordered spaces. We show that it is a normalized topological and give characterization zero-dimensionality D-connectedness in Moreover, characterize explicitly each T0, T1, pre-T2, T2 NT2 Finally, examine how these are related to other full subcategory Ti(pre-T2(L-Prord)) (i=0,1,2) pre-T2(L-Prord), Ti (L-Prord) (i=1,2) L-Prord isomorphic.

The paper provides a quantitative algebraic analysis of a BB’84-type quantum key distribution protocol. The analysis is done in an algebraic setting, where classical and quantum variables form a module for the quantale formed from the communication and quantum actions. The module-quantale pair is endowed with sup-maps that encode uncertainties of agents involved in the protocol, about the varia...

Assuming that B is a full A∞-subcategory of a unital A∞-category C we construct the quotient unital A∞-category D =‘C/B’. It represents the A u ∞-2-functor A 7→ A∞(C,A)modB, which associates with a given unital A∞-category A the A∞-category of unital A∞-functors C → A, whose restriction to B is contractible. Namely, there is a unital A∞-functor e : C → D such that the composition B →֒ C e −→ D i...