Homotopy Theory of ( ,1)-Categories

An introductory treatment to the homotopy theory of homotopical categories, presenting several models and comparisons between them.

List of contents

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.

About the author

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.

Summary

Homotopical or (8,1)-categories have become a significant framework in many areas of mathematics. This book gives an introduction to the different approaches to these structures and the comparisons between them from the perspective of homotopy theory.

Product details

• Authors: Julia E. Bergner, Julia E. (University of Virginia) Bergner, BERGNER JULIA E.
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Paperback / Softback
• Released: 31.03.2018
• EAN: 9781107499027
• ISBN: 978-1-107-49902-7
• No. of pages: 284
• Series: London Mathematical Society Student Texts; London Mathematical Society St; London Mathematical Society Student Texts; London Mathematical Society St
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Basic principles; MATHEMATICS / Logic, Mathematical logic, Algebraic Topology