Alexander Berglund: Infinity-categories

I will give an introduction to infinity-categories (quasi-categories) following the first sections of [L] and Appendix 9.1 of [G]. Our goal is to understand constructions that are relevant for the definition of factorization homology, such as the homotopy coherent nerve, overcategories, and homotopy pullbacks. (We will see how far we get, doing all this may require more than one lecture.)

[G] G.Ginot, Notes on factorization algebras, factorization homology and applications, http://arxiv.org/abs/1307.5213

[L] J.Lurie, Higher Topos Theory, http://www.math.harvard.edu/~lurie/