EVENT DETAILS AND ABSTRACT

Title: Three models for the homotopy theory of homotopy theories
Speaker: Julie Bergner
Speaker Info: University of Notre Dame
Brief Description:
Special Note:
Abstract:

Given any model category, or more generally, any homotopy theory, one can obtain from it a simplicial category which encodes all the homotopy theoretic information of the original homotopy theory. Having a model category structure on the category of all (small) simplicial categories is then a first step in studying the "homotopy theory of homotopy theories." While this model category structure does exist with appropriate weak equivalences, it would be helpful to find Quillen equivalent model category structures in which calculations are easier. I will discuss the simplicial category model category structure as well as two model structures which are Quillen equivalent to it: the complete Segal space model category structure on simplicial spaces and the Segal category model category structure on Segal precategories