We introduce homotopy coherent nerves of Kan-enriched categories. We discuss homotopy theory of Kan complexes and how composition is performed inside infinity-categories. For this, we introduce the
We define the notion of infinity-categories and Kan complex using observations from the previous talk. A process, called the nerve construction, producing infinity-categories from usual categories will be introduced and we will set dictionaries between them. Infinity-categories of functors will be introduced as well.
