SoSe 17: Infinity Categories
Shane Kelly
Additional information / Pre-requisites
Aimed at: Bachelor and masters students
Background: Strictly speaking, there is no necessarily background knowledge as we will follow Lurie's quasi-category approach which is self-contained. However, prior exposure to topology in some form is helpful.
Comments
Higher category theory lies in the intersection of two major developments of 20th century mathematics: topology and category theory. It provides a framework for settings where the morphisms between two objects form not just a set but a topological space, and is one of the best languages for modern homological algebra and sheaf theory.
Despite being a new discipline, higher category theory has already found spectacular applications across mathematics, such as Lurie's proof of the cobordism hypothesis (in Mathematical Physics), and Gaitsgory-Lurie's work on Weil's Tamagawa number conjecture (in Number Theory), not to mention applications in Geometric Langlands, K-theory, Mirror Symmetry, Knot Theory / Floer Homology...
This reading seminar will gently introduce some of the main concepts of higher category theory as developed by Lurie. By the end of the seminar, the student will be familiar enough with infinity categories that they can navigate texts written in this new language.
For more information see:
http://www.mi.fu-berlin.de/users/shanekelly/InfinityCategories2017SS.html
This reading seminar will complement the course Categories and Homotopy Theory 19234201.
Suggested reading
Course texts:
1. A short course on 8-categories by Groth
2. Higher topos theory by Lurie
3. Higher algebra by Lurie
11 Class schedule
Regular appointments