Infinity category theory lies in the intersection of two major developments of 20th century mathematics: topology and category theory. Category theory is a very powerful framework to organize and unify mathematical theories. Infinity category theory extends this framework to settings where the morphisms between two objects form not a set but a topological space (or a related object like a chain complex). This situation arises naturally in homological algebra, algebraic topology and sheaf theory. 

This reading seminar will recall the foundational ideas of usual category theory and then make the transition to homotopical algebra and infinity categories. 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.

A short course on ∞-categories by Groth,

Higher topos theory by Lurie,

Higher algebra by Lurie

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.

Literature:

A short course on ∞-categories by Groth,

Higher topos theory by Lurie,

Higher algebra by Lurie