Philip Hackney: Properads and Infinity Properads

Properads are an extension of the notion of operad which allow one to model structures with many-to-many operations, such as various kinds of bialgebras. In the first part of this talk we will discuss the concept in detail and provide some examples. In the second part we will present models for up-to-homotopy versions of properads, including properadic analogues of quasi-categories and simplicial categories.