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The homotopy theory of ([infinity symbol], 1)-categories

Author: Julia E Bergner; Cambridge University Press.
Publisher: Cambridge, UK : Cambridge University Press, 2018. ©2018
Series: London Mathematical Society student texts, 90.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Bergner, Julia Elizabeth.
Homotopy theory of ([infinity symbol],1)-categories.
Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2018
(DLC) 2018285687
(OCoLC)1003821934
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Julia E Bergner; Cambridge University Press.
ISBN: 9781316181874 1316181871
OCLC Number: 1030782653
Description: 1 online resource (xiv, 273 pages) : illustrations
Contents: Models for homotopy theories --
Simplicial objects --
Topological and categorical motivation --
Simplicial categories --
Complete Segal spaces --
Segal categories --
Quasi-categories --
Relative categories --
Comparing functors to complete segal spaces --
Variants on (∞, 1)-categories.
Series Title: London Mathematical Society student texts, 90.
Responsibility: Julia E. Bergner, University of Virginia.

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  Read more...

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'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 Read more...

 
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