Categories and infinitycategories
Organisation:
Time: Do 16:0018:00
First meeting: 18.10.2018
Room: KöLu2426/SR 006 Neuro/Mathe (KöniginLuiseStr. 24 / 26)
Summary:
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.
References:
For ordinary category theory:

An introduction to Homological Algebra, C.Weibel
For infinitycategory theory:

Higher topos theory, J.Lurie

Higher algebra, J.Lurie
Planning:
The above program contains at the moment the detailed overview of the first nine talks. The rest of the seminar will depend on the participants’ interests.