The homotopy theory of infinity, 1-categories

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Mathematics - Algebra
The homotopy theory of infinity,...

The homotopy theory of infinity, 1-categories

Name: The homotopy theory of infinity, 1-categories
ISBN: 9781316181874

Bergner, Julia Elizabeth

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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.
Abstract: Homotopical or ( ,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.

الفئات:

Mathematics - Algebra

عام:

2018

الناشر:

Cambridge University Press

اللغة:

english

الصفحات:

273

ISBN 10:

1316181871