© 2021

Introduction to Infinity-Categories


Part of the Compact Textbooks in Mathematics book series (CTM)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Markus Land
    Pages 249-272
  3. Back Matter
    Pages 273-296

About this book


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.


infinity-categories functors limits and colimits adjunctions adjoint functor theorems

Authors and affiliations

  1. 1.Department of Mathematical SciencesUniversity of CopenhagenCopenhagenDenmark

About the authors

​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.

Bibliographic information

  • Book Title Introduction to Infinity-Categories
  • Authors Markus Land
  • Series Title Compact Textbooks in Mathematics
  • Series Abbreviated Title Compact Textbooks in Mathematics
  • DOI
  • Copyright Information The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-030-61523-9
  • eBook ISBN 978-3-030-61524-6
  • Series ISSN 2296-4568
  • Series E-ISSN 2296-455X
  • Edition Number 1
  • Number of Pages IX, 296
  • Number of Illustrations 389 b/w illustrations, 1 illustrations in colour
  • Topics Category Theory, Homological Algebra
  • Buy this book on publisher's site