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Birkhäuser

Introduction to Infinity-Categories

  • Textbook
  • © 2021

Overview

Authors:
  1. Markus Land

    1. Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark

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  • Presents a high-level topic in an accessible style
  • Includes exercises
  • Leads the reader from the theory basics to more advanced results

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-ix
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  2. Categories, Simplicial Sets, and Infinity-Categories

    • Markus Land
    Pages 1-95

  3. Joyal’s Theorem, Applications, and Dwyer–Kan Localizations

    • Markus Land
    Pages 97-161

  4. (Co)Cartesian Fibrations and the Construction of Functors

    • Markus Land
    Pages 163-203

  5. Limits, Colimits, and Quillen’s Theorem A

    • Markus Land
    Pages 205-247

  6. Adjunctions and Adjoint Functor Theorems

    • Markus Land
    Pages 249-272

  7. Back Matter

    Pages 273-296
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Keywords

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.

Reviews

“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)

Authors and Affiliations

  • Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark

    Markus Land

About the author

​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

  • DOI: https://doi.org/10.1007/978-3-030-61524-6

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

  • Softcover ISBN: 978-3-030-61523-9Published: 22 April 2021

  • eBook ISBN: 978-3-030-61524-6Published: 21 April 2021

  • 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

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