Introduction to Infinity-Categories

Markus Land (Autor)

Buch | Softcover

IX, 296 Seiten

2021 | 1st ed. 2021
Springer International Publishing (Verlag)
9783030615239 (ISBN)

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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.

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.

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.

"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)

“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)

Erscheinungsdatum	24.04.2021
Reihe/Serie	Compact Textbooks in Mathematics
Zusatzinfo	IX, 296 p. 390 illus., 1 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	474 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Schlagworte	adjoint functor theorems • adjunctions • functors • infinity-categories • limits and colimits
ISBN-13	9783030615239 / 9783030615239
Zustand	Neuware