The Homotopy Theory of (?,1)-Categories
Published on 21. February 2018
978-1-108-56504-2 (ISBN)
Description
The notion of an (?,1)-category has become widely used in homotopy theory, category theory, and in a number of applications. There are many different approaches to this structure, all of them equivalent, and each with its corresponding homotopy theory. This book provides a relatively self-contained source of the definitions of the different models, the model structure (homotopy theory) of each, and the equivalences between the models. While most of the current literature focusses on how to extend category theory in this context, and centers in particular on the quasi-category model, this book offers a balanced treatment of the appropriate model structures for simplicial categories, Segal categories, complete Segal spaces, quasi-categories, and relative categories, all from a homotopy-theoretic perspective. Introductory chapters provide background in both homotopy and category theory and contain many references to the literature, thus making the book accessible to graduates and to researchers in related areas.
Reviews / Votes
'The writing is accessible, even for students, and the ideas are clear. The author gives references for every claim and definition, with the added advantage that some technical [lengthy] points can be left out to avoid burying the ideas.' Najib Idrissi, zbMATHMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
File size
1,64 MB
ISBN-13
978-1-108-56504-2 (9781108565042)
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Schweitzer Classification
Other editions
Additional editions
Julia E. Bergner
The Homotopy Theory of (?,1)-Categories
Book
03/2018
Cambridge University Press
€150.30
Shipment within 15-20 days
Person
Julia E. Bergner is an Associate Professor at the University of Virginia. She has written several foundational papers in the area of (?, 1)-categories, and is currently working on generalizations to higher (?, n)-categories, (?, 1)-operads, and equivariant versions. She currently has an NSF CAREER award to investigate algebraic and geometric applications of these kinds of structures. This book was inspired by the notes from a series of lectures on 'The Homotopy Theory of Homotopy Theories' presented in Israel in 2010, with talks given by the author and a number of other participants.
Content
Preface; Acknowledgments; Introduction; 1. Models for homotopy theories; 2. Simplicial objects; 3. Topological and categorical motivation; 4. Simplicial categories; 5. Complete Segal spaces; 6. Segal categories; 7. Quasi-categories; 8. Relative categories; 9. Comparing functors to complete Segal spaces; 10. Variants on (?, 1)-categories; References; Index.
