A Compositional Coalgebraic Model of a Fragment of Fusion Calculus

This work is a further step in exploring the labelled transitions and bisimulations of fusion calculi. We follow the approach developed by Turi and Plotkin for lifting transition systems with a syntactic structure to bialgebras and, thus, we provide a compositional model of the fusion calculus with explicit fusions. In such a model, the bisimilarity relation induced by the unique morphism to the final coalgebra coincides with fusion hyperequivalence and it is a congruence with respect to the operations of the calculus. The key novelty in our work is to give an account of explicit fusions through labelled transitions. In this short essay, we focus on a fragment of the fusion calculus without recursion and replication.