I shall give the third in a series of talks on the unification of different parts of mathematics at the University of Gdańsk. The talk shall take place on 13 December 2022 at 10:15 local time in room 130, Faculty of Mathematics, Physics, and Informatics.

**Abstract.** One of the central incentives of the rise of category theory was to understand a mathematical structure in the context of a family of structures of a similar kind, allowing one to understand how these structures are interrelated. Nearly eight decades later, the modal model theory was introduced, with precisely that same intention in mind, albeit a completely different approach. I shall now provide a framework that unifies the two perspectives.