Alice Hedenlund: Infinity-categories
Time: Fri 2020-01-31 10.15 - 12.00
Lecturer: Alice Hedenlund (University of Oslo)
Location: Room 3418, KTH
This is the first talk of the seminar on algebraic K-theory and derived algebraic geometry .
Category theory is an useful and powerful way of dealing with information about mathematical objects. In the sense of category theory we talk about two mathematical objects as ”the same” if they are isomorphic. However, there are many situations where a weaker notion of "the same" is more useful, not only when working with categories themselves as the mathematical objects of interest. To deal with this, one introduces the concept of higher categories. In this talk, we focus on (oo,1)-categories, which we will abusively refer to simply as oo-categories. There are many equivalent models to describe these, and we will here take the approach of quasi-categories, simplicial sets with certain lifting properties, as developed by Joyal and Lurie. In this model, we show how to make sense of many categorical notions, including, but not limited to, functors, natural transformations, adjunctions, and equivalences in and between categories.