Graduate Student Seminar - Brandon Doherty (Math)
Room: 107
Title: A Model Structure for Cubical Categories
Speaker: Brandon Doherty
Abstract: Simplicial categories, categories enriched over simplicial sets, are one of the most well-known models for the theory of ($\infty$,1)-categories. Their homotopy theory is studied by means of a model structure on the category of simplicial categories, due to Bergner. Recently there has been some interest in categories enriched over cubical sets as an alternative model for ($\infty$,1)-categories. In this talk, I will discuss a model structure on the category of cubical categories which is analogous to the Bergner model structure for simplicial categories. If time permits, I will also discuss an adjunction between the categories of simplicial sets and cubical categories, due to Kapulkin and Voevodsky, and sketch the proof that it is a Quillen adjunction when the category of simplicial sets is equipped with the Joyal model structure.
As always, great food, coffee and drinks will be provided!
We encourage your participation in the seminar to provide continuity to this project.