We analyse two complementary methods for obtaining models of typed process calculi, in the form of interaction categories. These methods allow adding new features to previously captured notions of process and of type, respectively. By combining them, all familiar examples of interaction categories, as well as some new ones, can be built starting from some simple familiar categories. Using the presented constructions, interaction categories can be analysed without fixing a set of axioms, merely in terms of the way in which they are specified --- just like algebras are analysed in terms of equations and relations, independently on abstract characterisations of their varieties.

To use quantum mechanical behavior for computing has been proposed by Feynman. Shor gave an algorithm for the quantum computer which raised a big stream of research. This was because Shor's algorithm did reduce the yet assumed exponential complexity of the security relevant factorization problem, to a quadratic complexity if quantum computed. In the paper a short introduction to quantum mechanics can be found in the appendix. With this material the operation of the quantum computer, and the ideas of quantum logic will be explained. The focus will be the argument that a connection of quantum logic and linear logic is the right type theory for quantum computing. These ideas are inspired by Vaughan Pratt's view that the intuitionistic formulas argue about states (i.e physical quantum states) and linear formulas argue about state transformations (i.e computation steps). 1 Introduction A calculus for programs on quantum computers is strongly missed. Here we present the material t...

Deep categorical analyses of various aspects of concurrency have been developed, but a uniform categorical treatment of the very first concepts seems to be hindered by the fact that the existing representations of processes as bisimilarity classes do not provide a sufficient account of computational morphisms. In the present paper, we describe a category of processes modulo strong bisimulations, with the bisimilarity preserving simulations as morphisms, and show that it is isomorphic to --- and can be conveniently represented by --- a subcategory of transition systems, with graph morphisms. The representative of each process and every morphism can effectively calculated, using coinduction (but with no reference to proper classes). The method is applicable to richer notions of a process as well, which are studied in the sequel. 1 Introduction A process is usually presented as some kind of a labelled graph. In fact, any directed graph with labelled edges and a distinguished initial node...