Introduction to Infinity-Categories

​Markus Land is a lecturer at the University of Regensburg and a guest researcher at the University of Copenhagen in the academic year 2019/2020.

“This book is a concise and rather comprehensive introduction to the theory of ∞-categories, aimed at a wide audience. … The material developed in this book mostly originates from the work of Joyal and Lurie. It is presented here in a fresh, streamlined, and accessible way. The length and style of this book make it ideally suited for a lecture course or seminar on ∞-categories. … Finally, a nice collection of exercises is included as an appendix.” (Gijs Heuts, Mathematical Reviews, July, 2022)

• Preface.- Categories, simplicial sets, and in nity-categories.- Joyal's theorem, applications, and Dwyer-Kan localizations.- (Co)Cartesian brations and the construction of functors.- Limits and Colimits.- Adjunctions and adjoint functor theorems.- Exercises.