We present a model of classical linear logic based on the notion of strong stability that was introduced in [BE], a work about sequentiality written jointly with Antonio Bucciarelli.

Abstract: We study the relations between the invariants τRT, τHKR, and τL of Reshetikhin-Turaev, Hennings-Kauffman-Radford, and Lyubashenko, respectively. In particular, we discuss explicitly how τL specializes to τRT for semisimple categories and to τHKR for Tannakian categories. We give arguments for that τL is the most general invariant that stems from an extended TQFT. We introduce a canonical, central element, Q, for a quasi-triangular Hopf algebra, A, that allows us to apply the Hennings algorithm directly, in order to compute τRT, which is originally obtained from the semisimple trace-subquotient of A − mod. Moreover, we generalize Hennings ’ rules to the context of cobordisms, in order to obtain a TQFT for connected surfaces compatible with τHKR. As an application we show that, for lens spaces and A = Uq(sl2), the ratio of τHKR and τRT is the order of the first homology group. In the course of this paper we also outline the topology and the algebra that enter invariance proofs, which contain no reference to 2-handle slides, but to other moves that are local. Finally, we give a list of open questions regarding cellular invariants, as defined by Turaev-Viro, Kuperberg, and others, their relations among

This paper describes a mixed induction/co-induction property of relations on recursively defined domains. We work within a general framework for relations on domains and for actions of type constructors on relations introduced by O'Hearn and Tennent [20], and draw upon Freyd's analysis [7] of recursive types in terms of a simultaneous initiality/finality property. The utility of the mixed induction/co-induction property is demonstrated by deriving a number of families of proof principles from it. One instance of the relational framework yields a family of induction principles for admissible subsets of general recursively defined domains which extends the principle of structural induction for inductively defined sets. Another instance of the framework yields the co-induction principle studied by the author in [22], by which equalities between elements of recursively defined domains may be proved via `bisimulations'. 1 Introduction A characteristic feature of higher-order functional lan...

this paper consists of lifting the --- categorically --- equivalent descriptions of physical systems by a (i) `state space' or a (ii) `property lattice' --- see [14,20,25,26] --- to an asymmetrical --- i.e., not anymore isomorphic --- duality on the level of: (i)

Abstract. We continue our study of the general theory of possibly nonselfadjoint algebras of operators on a Hilbert space, and modules over such algebras, developing a little more technology to connect ‘nonselfadjoint operator algebra ’ with the C ∗ −algebraic framework. More particularly, we make use of the universal, or maximal, C ∗ −algebra generated by an operator algebra, and C ∗ −dilations. This technology is quite general, however it was developed to solve some problems arising in the theory of Morita equivalence of operator algebras, and as a result most of the applications given here (and in a companion paper) are to that subject. Other applications given here are to extension problems for module maps, and characterizations of C ∗ −algebras. * Supported by a grant from the NSF. The contents of this paper were announced at the January 1999 meeting of the American Mathematical Socety. 1 2 DAVID P. BLECHER 1. Introduction- Modules

Let X be a topological space. Then we may define the fundamental groupoid nX and also the quotient groupoid (nX)/N for N any wide, totally disconnected, normal subgroupoid N of nX (1). The purpose of this note is to show that if X is locally path-connected and semi-locally 1-connected, then the topology of X

Infinite contexts and their corresponding lattices are of theoretical and practical interest since they may o#er connections with and insights from other mathematical structures which are normally not restricted to the finite cases. In this paper we establish a systematic connection between formal concept analysis and domain theory as a categorical equivalence, enriching the link between the two areas as outlined in [25].

A unified scheme for treating generalized superselection sectors is proposed on the basis of the notion of selection criteria to characterize states of relevance to each specific domain in quantum physics, ranging from the relativistic quantum fields in the vacuum situations with unbroken and spontaneously broken internal symmetries, through equilibrium and non-equilibrium states to some basic aspects in measurement processes. This is achieved by the help of c → q and q → c channels: the former determines the states to be selected and to be parametrized by the order parameters, and the latter provides the physical interpretations of selected states in terms of order parameters. This formulation extends...

Abstract. We show that two operator algebras are strongly Morita equivalent (in the sense of Blecher, Muhly and Paulsen) if and only if their categories of operator modules are equivalent via completely contractive functors. Moreover, any such functor is completely isometrically isomorphic to the Haagerup tensor product ( = interior tensor product) with a strong Morita equivalence bimodule.

. Functional languages are based on the notion of application: programs may be applied to data or programs. By application one may define algebraic functions; and a programming language is functionally complete when any algebraic function f(x 1 ,...,x n ) is representable (i.e. there is a constant a such that f(x 1 ,...,x n ) = (a . x 1 . ... . x n ). Combinatory Logic is the simplest type-free language which is functionally complete. In a sound category-theoretic framework the constant a above may be considered as an "abstract gödel-number" for f, when gödel-numberings are generalized to "principal morphisms", in suitable categories. By this, models of Combinatory Logic are categorically characterized and their relation is given to lambda-calculus models within Cartesian Closed Categories. Finally, the partial recursive functionals in any finite higher type are shown to yield models of Combinatory Logic. ________________ (+) Theoretical Computer Science, 70 (2), 1990, pp.193-211. A p...