Operads are a useful tool in classifying algebraic objects. Monoidal categories are algebraic objects in the categories of categories. One may require that the monoidal product of a category be commutative, up to isomorphism. This commutativity can even be governed by a sequence of groups {G_n}, in the sense that these groups act on iterated monoidal products exhibiting commutativity isomorphisms between the different permutations. In this talk, I will explain the construction of certain operads in the category of groupoids that allow us to define these G-monoidal categories.

Bio: Olivia Borghi (she/her) is a Ph.D. candidate at the University of Melbourne in Naarm (Melbourne), Australia. Before attending Melbourne she received her masters in pure mathematics from the University of Washington in Seattle, USA. Olivia's research interests are in homotopy theory, specifically in higher operads and monoidal categories as well as how they connect to quantum algebra. She is now and always a vocal advocate for diversity, equity and inclusion in mathematics.