Lecture group on Higher Categories

The ultimate goal of this lecture group is to understand what is a stable \infty-category, as defined in the first chapter of Higher Algebra [HA] by Lurie. To get to this we will follow the quite recent book of Cisinski Higher Categories and Homotopical Algebra in order to get a good understanding of what an \infty-category is. We would like to thank Robin Carlier for his really precise comments on this latter book.

Date and timeSpeakerTitleNotes
11/12/21 at 16:30SwannIntroduction and organisation.
Chapter 1: Simplicial Sets and presheaves.		Notes
17/12/21 at 16:30SofianChapter 1 : Cellular decompositions
, nerves, ∞-categories and the Boardmann-Vogt construction.
21/01/2022 at 16:30DavidChapter 2 : Factorisation systems and Model Categories Notes
28/01/22 at 16:30SwannChapter 2 :Cylinders, Derived functor and homotopical limits
4/02/22LucasChapter 2 : Model Structure ex nihilo
11/02/22SofianEnd of Chapter 2 : Absolute weak equivalences, and remaining bits of chapter 1.
27/02/22TanguyChapter 3 : Kan fibrations and Kan-Quillen model structureNotes
04/03/22SwannChapter 3 : Inner Anodyne extensions and the Joyal model category structure
11/03/22LucasChapter 3 : Left and right fibrations, joins and slices. Remaining bits of 3.3. Examples Session.
8/04/22SwannHeuristic of certain fibrations. Chapter 3 : Invertible natural transformationsNotes
15/04/22Postponed
22/04/22SofianChapter 3 : Invertible natural transformations, \infty-categories as fibrant objects.
29/04/22MarwanChapter 3: The Boardman-Vogt construction revisited. Examples session.
6/05/22SwannExample of invertible natural transformation in small dimension. Overview of the cotangent complex and André-Quillen (co)homology
20/05/22LucasModel structure on simplicial categories, following Quillen Homotopical Algebra ([Qui67])Notes
13/05/22Postponed
3/06/22LucasCohomology in abstract categories and the cotangent compelx, following [Qui70]
10/06/22SwannDeformations with the cotangent complex

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