EVENT DETAILS AND ABSTRACT

Title: On higher versions of Quillen's theorem B
Speaker: Emanuele Dotto
Speaker Info: MIT
Brief Description:
Special Note: An informal talk before tomorrow's Midwest Topology Seminar
Abstract:

The famous Theorem B of Quillen gives, under certain conditions, a categorical model for the homotopy fiber of the geometric realization of a functor. This result has been extended in later work of Barwick and Kan to categorical models for general homotopy pullbacks. We will interpret Quillen's condition as a "quasi-fibrancy" condition for the pullback diagram, and extend these results to diagrams of categories shaped over finite posets. In particular, this provides a model for homotopy limits of punctured cubes. These techniques generalize equivariantly, when a finite group acts on the whole diagram.