The Homotopy Theory of (∞,1)-Categories (London Mathematical Society Student Texts, Series Number 90) 1st Edition by Julia E. Bergner (PDF)

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.

User’s Reviews

Editorial Reviews: Review ‘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, zbMATH Book Description An introductory treatment to the homotopy theory of homotopical categories, presenting several models and comparisons between them. 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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Es un buen libro, me ha servido mucho

⭐

⭐Thanks to professor

⭐Excellent book on homotopy theory

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