Wiring Diagrams, a categorical formalism for systems modeling
In this talk, we present a categorical framework for understanding and analyzing systems of systems in a broad sense. The advantages of such an approach lie on `compositionality', namely the fact that we can apply our analysis to the subsystems independently, and the results can be composed in a specific sense. Our base formalism is that of open systems (that take in, process, and send out material) as "algebras for the monoidal category of labeled boxes and wiring diagrams" which will be discussed in detail. An arbitrary interconnection of subsystems can be mathematically modeled in a uniform way, and the categorical machinery produces the function and/or behavior of the total system given the functions and/or behaviors of the components. Examples of such systems-as-algebras are Moore Machines (automata) as well as continuous dynamical systems or even behavioral contracts on systems.
Christina Vasilakopoulou is a researcher at the Department of Mathematics, University of Patras, Greece. She obtained her PhD in Pure Mathematics (Category Theory) at the University of Cambridge, UK and since then she has worked as a PostDoc with various research groups in MIT, ULB, UCR and more. Her interests lie both in theory and applications of categories in relation to algebra, database theory and systems modeling.