The homotopy theory of ([∞],1)-categories
著者
書誌事項
The homotopy theory of ([∞],1)-categories
（London Mathematical Society student texts, 90）
Cambridge University Press, 2018
- : hardcover
- : pbk
- タイトル別名
-
The homotopy theory of ([infinity symbol],1)-categories
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注記
Includes bibliographical references (p. 261-266) and indexes
内容説明・目次
内容説明
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.
目次
- 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.
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