Introduction to Infinity-Categories

1. Auflage 2021
ISBN: 978-3-030-61523-9
Verlag: Springer International Publishing

Buch, Englisch, 296 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 470 g

Reihe: Compact Textbooks in Mathematics

This textbook is an introduction to the theory of infinity-categories, a tool used in many aspects of modern pure mathematics. It treats the basics of the theory and supplies all the necessary details while leading the reader along a streamlined path from the basic definitions to more advanced results such as the very important adjoint functor theorems.

The book is based on lectures given by the author on the topic. While the material itself is well-known to experts, the presentation of the material is, in parts, novel and accessible to non-experts. Exercises complement this textbook that can be used both in a classroom setting at the graduate level and as an introductory text for the interested reader.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Land, Markus

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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.

Über Autor(innen)

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.