15/05/2026, 11:00 — 12:00 —
Room P3.10, Mathematics Building
Luca Mesiti, Stellenbosch University
What is 2-dimensional categorical algebra?
Categorical algebra is a fundamental branch of mathematics that lies at the intersection of category theory and algebra. On the one hand, it captures the fruitful properties and structures studied in algebra via category theory. On the other hand, it investigates the global categorical properties that algebraic objects enjoy when collected together. Both these endeavors are essential to extend and transport the fundamental concepts and theorems of algebra to different and broader settings. In this talk, we present an innovative theory that generalizes categorical algebra to the framework of 2-dimensional category theory. This has the notable advantage that the second dimension can be used both to weaken conditions that are too strict in nature and to refine algebraic invariants, obtaining a richer theory which encompasses a broader range of examples. Furthermore, 2-dimensional categorical algebra is essential to effectively compare different algebraic categories with each other.
This talk is based on a joint work with Elena Caviglia and Zurab Janelidze.
