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The theory of reactive systems, introduced by Leifer and Milner and previously extended by the authors, allows the derivation of well-behaved labelled transition systems (LTS) for semantic models with an underlying reduction semantics. The derivation procedure requires the presence of certain colimits (or, more usually and generally, bicolimits) which need… (More)

We introduce G-relative-pushouts (GRPO) which are a 2-categorical generalisation of relative-pushouts (RPO). They are suitable for deriving labelled transition systems (LTS) for process calculi where terms are viewed modulo structural congruence. We develop their basic properties and show that bisimulation on the LTS derived via GRPOs is a congruence,… (More)

We present a new labelled transition system (lts) for the ambient calculus on which ordinary bisimilarity coincides with contex-tual equivalence. The key feature of this lts is that it is the fruit of ongoing work on developing a systematic procedure for deriving ltss in the structural style from the underlying reduction semantics and ob-servability.… (More)

We use the framework of biorthogonality to introduce a novel semantic definition of the concept of barb (basic observable) for process calculi. We develop a uniform basic theory of barbs and demonstrate its robustness by showing that it gives rise to the correct observables in specific process calculi which model synchronous, asynchronous and broadcast… (More)

Groupoidal relative pushouts (GRPOs) have recently been proposed by the authors as a new foundation for Leifer and Milner's approach to deriving labelled bisimulation congruences from reduction systems. In this paper, we develop the theory of GRPOs further, proving that well-known equivalences, other than bisimulation, are congruences. To demonstrate the… (More)

Bialgebras and Frobenius algebras are different ways in which monoids and comonoids interact as part of the same theory. Such theories feature in many fields: e.g. quantum computing, compositional semantics of concurrency, network algebra and component-based programming. In this paper we study an important sub-theory of Coecke and Duncan's ZX-calculus,… (More)

We introduce the theory IH R of interacting Hopf algebras, parametrised over a principal ideal domain R. The axioms of IH R are derived using Lack's approach to composing PROPs: they feature two Hopf algebra and two Frobenius algebra structures on four different monoid-comonoid pairs. This construction is instrumental in showing that IH R is isomorphic to… (More)

We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved. Many types of graphical structures used in computer science are shown to be examples of adhesive categories. Double-pushout graph rewriting generalises well to rewriting on arbitrary adhesive categories.

G-relative pushouts (GRPOs) have recently been proposed by the authors as a new foundation for Leifer and Milner's approach to deriving labelled bisimulation congruences from reduction systems. This paper develops the theory of GRPOs further, arguing that they provide a simple and powerful basis towards a comprehensive solution. As an example, we construct… (More)