Compositionality via 2-algebra
A complex system may be designed modularly by putting together interacting component subsystems. Since analyses of complex systems can often scale very poorly with their size, it pays to use the modular structure of such systems to divide the task of analysis across the component subsystems.
Many analyses of systems may be encoded as homomorphism search problems between systems of the same sort. This suggests attending to categories of systems and their homomorphisms. In this talk, we’ll consider the modular structure of a class of systems as a 2-algebra — an algebraic structure on categories of systems (and their interfaces and interaction patterns). We’ll see compositionality theorems as (lax) homomorphisms of these 2-algebraic structures, and survey a number of techniques for proving them using 2-categorical algebra.