Algebraic K-Theory Seminar
Jonathan Beardsley
Georgia Tech
On Koszul Duality in Higher Topoi
Abstract: In this talk, I will describe joint work with Maximilien Péroux on understanding Koszul duality in ∞-topoi and n-topoi. The main theorem of this work is that given a group object G of an n-topos, there is an equivalence of ∞-categories between the category of G-modules in that topos and the category of BG-comodules, where BG is the classifying object for G-torsors. In particular, given any loop space ΩX, and any ∞-topos T, there is an equivalence of ∞-categories between objects of T with an ΩX-action, the slice topos over the "constant sheaf" valued in BΩX, and objects with a BΩX-coaction. This is a generalization of the classical equivalence between G-spaces and spaces over BG for G a topological group.
Wednesday November 13, 2019 at 11:00 AM in 1227 SEO