# Topology Seminar- Monoidal categories enriched in braided monoidal categories

Speaker: David Penneys (Ohio State University)

Time: Monday, November 13, 2017, 12:15-1:15

Title: Monoidal categories enriched in braided monoidal categories

Place: Rome 771

Abstract: While the symmetries of classical mathematical objects form groups, the symmetries of ‘quantum’ mathematical objects such as subfactors and quantum groups form more general objects which are best axiomatized as monoidal categories. Early in the study of monoidal categories, Eilenberg and Kelly defined the notion of a category enriched in a monoidal category. Recently, there has been a lot of interest in super monoidal categories, which are enriched in super vector spaces. These enriched categories are examples of monoidal categories enriched in symmetric monoidal categories. In a recent article with Morrison (arXiv:1701.00567), we introduce the notion of a monoidal category enriched in a braided monoidal category V, which is not assumed to be symmetric. We then classify V-monoidal categories in terms of strictly unital oplax braided monoidal functors from V to the centers of ordinary monoidal categories

Abstract: While the symmetries of classical mathematical objects form groups, the symmetries of ‘quantum’ mathematical objects such as subfactors and quantum groups form more general objects which are best axiomatized as monoidal categories. Early in the study of monoidal categories, Eilenberg and Kelly defined the notion of a category enriched in a monoidal category. Recently, there has been a lot of interest in super monoidal categories, which are enriched in super vector spaces. These enriched categories are examples of monoidal categories enriched in symmetric monoidal categories. In a recent article with Morrison (arXiv:1701.00567), we introduce the notion of a monoidal category enriched in a braided monoidal category V, which is not assumed to be symmetric. We then classify V-monoidal categories in terms of strictly unital oplax braided monoidal functors from V to the centers of ordinary monoidal categories

Bio:

2016–Present The Ohio State University, Ohio, USA. Assistant professor

2014-16 University of California, Los Angeles, California, USA. Assistant adjunct professor

2012-14 University of Toronto, Ontario, Canada. Mathematics postdoctoral fellow Postdoctoral supervisors: Dror Bar-Natan and George Elliott

2005-12 University of California, Berkeley, California, USA. Mathematics Ph.D.

Advisor: Vaughan F.R. Jones Dissertation: “Planar structure for inclusions of finite von Neumann algebras”

2001-5 The George Washington University, Washington, D.C., USA, Mathematics, B.A., Ruggles Prize 2003 and 2005

Physics, B.S., Howard Hughes Fellow in Bioinformatics 2004 Chemistry,

B.S., George Gamow Fellow 2003 Columbian School Distinguished Scholar, Summa Cum Laude, Phi Beta Kappa.