Infinity Categories

What it is about

You will learn the fundamentals and central concepts of ∞-category theory, especially in the presentation as quasi-categories (simplicial sets with certain lifting properties). In the end you can apply the key constructions such as fibrations, limits/colimits, adjunctions and the Grothendieck construction and you will be able to familiarize yourself with further literature and research.

What you will be able to do

• Understanding the definitions and fundamental properties of ∞-categories and ∞-groupoids
• Applying simplicial sets to describe higher categories
• Knowledge of comparison results (e.g. to simplicial categories and the coherent nerve)
• Understanding fibrations, limits, colimits and adjunctions in ∞-categories
• Applying the straightening/unstraightening correspondence (Grothendieck construction)
• Familiarity with the Yoneda lemmas and an introduction to Higher Algebra (derived algebra objects)

What the module consists of

• VorlesungPräsentation theoretischer Prinzipien und Beispiele; zentrale Einführung in die Konzepte
• Übung / TutoriumBesprechen und Lösen von Aufgaben zur Vertiefung und Anwendung der Vorlesungsinhalte

Teaching method

• TafelvortragVermittlung der theoretischen Grundlagen und detaillierter Beweise
• ÜbungsblätterVertiefung durch konkrete Aufgaben und Beispiele