Date: 2011-8-19, 3:00pm

Venue:Conference Hall 213, Science Building

Title: Higher groupoids and higher morphisms

Speaker: Prof. Chenchang Zhu

Georg-August-Universität Göttingen

Abstract: It is known that for groupoids carrying certain topology, for many purposes, usual groupoid morphisms will not be enough. One needs to consider bibundles (comparable to Hilbert bimodules in noncommutative geometry) as generalized morphisms. These bibundles sometimes are called Hilsum-Skandalis bibundles/bimodules. We extend this to higher groupoids with the language of Kan fibrations. In short, the nerve of an n-groupoid is a simplicial object with certain Kan conditions. Then two n-groupoids and the bibundles between them provide a simplicial object with Kan fibration over the simplicial 1-simplex. This method makes it easy to establish higher morphisms by adding the dimension of the simplex fibred over, thus eventually to a quasi-category of n-groupoids.