Bialgebraic foundations for the operational semantics of string diagrams

Turi and Plotkin's bialgebraic semantics is an abstract approach to specifying the operational of a system, by means distributive law between its syntax (encoded as monad) dynamics (an endofunctor). This setup instrumental in showing that semantic specification (a coalgebra) compositional. In this work, we use derive well-behaved structural string diagrams, graphical increasingly used study interacting systems across different disciplines. Our analysis relies on representing two-dimensional operations underlying diagrams various categories monad, their for monad. As proof concept, provide versatile diagrammatic language which has been model both signal flow graphs (control theory) Petri nets (concurrency theory).