Topology Seminar
Speaker: Udit Mavinkure, IIT Bombay
Host: Rekha Santhanam
Title: Quasicategories vs Segal spaces, Part 2
Time, day and date: 11:30:00 AM – 12:30:00 PM, Thursday, May 07
Venue: Room 215
Abstract: This is Part 2 in a series of 4 expository talks that will culminate in Joyal and Tierney's proof of two Quillen equivalences between the Joyal model structure for quasicategories and the Rezk model structure for complete Segal spaces, both of which present the homotopy theory of (oo,1)-categories.

In this second talk, we will look at quasicategories, which are simplicial sets satisfying the weak Kan condition (i.e. inner horns admit fillers). These generalize the notion of categories and furthermore are the fibrant objects in a model structure on the category of all simplicial sets where the weak equivalences generalize the notion of equivalences of categories. We will also look at relevant aspects of this model structure, called the Joyal model structure for quasicategories.