Title: Descent Theory and The Local Joyal Model Structure
Speaker: Nicholas Meadows (University of Western Ontario)
Abstract: We will introduce the local Joyal model structure, a model structure on simplicial presheaves in which the weak equivalences are maps which are ‘stalkwise’ weak equivalences in the Joyal model structure. We will give a simple characterization of descent with respect to the local Joyal model structure, which relies on the local analogue of the Rezk model structure.
Throughout, we will introduce various quasi-categorical constructions such as the core, slice, join and mapping spaces. We will explain how these interact with the local theory. As an application, we will prove a criterion for descent in terms of mapping space presheaves.
We will then explain how refinements of this criterion can be applied to give simplified proofs, and in some cases generalizations, of some of Simpson’s main results on higher stacks.
Seminar URL: https://people.math.osu.edu/valenzuelavasquez.2/hts/
