Universal Constructions: Drinking the Kool-Aid of the Universe
OTHER MATHEMATICS DEPARTMENT EVENTS: MATH TABLE
Mathematics is full of seemingly unrelated structures which can be unified via universal constructions. In this talk, we’ll dive into the concept of universality, revealing how universal properties—often seen as isolated tricks in contexts like kernels and free objects—provide deep connections across fields. By exploring examples accessible to all undergraduates, we will show how universal constructions simplify relationships, clarify definitions, and connect diverse areas of math. We will introduce fundamental category theoretic notions from the ground up. Come experience the transformative power and elegance that universal properties bring to mathematics. Once you’ve tasted this “Kool-Aid,” you may never see math the same way again.