Title: Basic constructions for the 1-category theory of ∞-categories
Abstract: I will start with my interpretation of one major motivation for homotopy theorists to work with ∞-categories and introduce a nowadays favorite model, i.e., quasi-categories, for these. Then I will discuss the first properties of the nerve and homotopy category construction and justify the viewpoint of 1-categories as ∞-categories. I will end with the definition of an (∞)-space in this framework and give the easier direction of its identification with a Kan complex. This talk is (almost entirely) based on the first two chapters of Charles' lecture notes for the higher cats course he offers every ~three semesters and the speaker hopes that her talk serves as a proper advertisement for its upcoming installment!
