00 2 Sup - lattice 2 - forms and quantales ∗

00 3 Sup - lattice 2 - forms and quantales ∗

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.

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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.

Sup-Lattice 2-Forms and Quantales

On Simple and Semisimple Quantales

In a recent paper [7], J. W. Pelletier and J. Rosický published a characterization of *-simple *-quantales. Their results were adapted for the case of simple quantales by J. Paseka in [5]. In this paper we present similar characterizations which do not use a notion of discrete quantale. We also show a completely new characterization based on separating and cyclic sets. Further we explain a link...

Equality in Linear Logic

1 Quantales In this section we introduce the basic deenitions and results of the theory of quantales (a good reference is Ros]). Quantales were introduced by Mulvey ((Mul]) as an algebraic tool for studying representations of non-commutative C-algebras. Informally, a quantale is a complete lattice Q equipped with a product distributive over arbitrary sup's. The importance of quantales for Linea...