Title:  Universal objects in vertex algebra theory

Abstract:   This is a sequel to my first talk on trialities of W-algebras. I will discuss the notion of universal objects, which are certain vertex algebras defined over commutative rings. They are useful for classifying vertex algebras with prescribed strong generating types. The two-parameter vertex algebra W(c,\lambda) which appears in the proof of the Gaiotto-Rapcak triality conjecture, is an example of such a universal object. I will give some further details about this construction and how it is used to prove the triality conjecture.