During the last three decades, coalgebras have emerged as the right mathematical model for studying state-based, dynamical systems from an abstract perspective. Coalgebras can uniformly capture the essence of different semantic models, their associated notions of equivalence and the logics used to reason about them, while abstracting away from the specifics of concrete settings. In my talk I will argue that this coalgebraic view can provide new insights, allow known techniques to be transferred to new settings, and even drive the discovery of new structures that can extend the reach of existing techniques. I will substantiate this claim with two examples: applications to program verification, and (initial steps towards) applications to reactive synthesis.

The talk is based on joint work with Anton Chernev, Helle Hansen, Clemens Kupke and Benjamin Plummer.