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London Mathematical Society Student Texts: Homotopy Theory of (1)-Categories by Julia E. Bergner (2018, Trade Paperback)

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About this product

Product Identifiers

PublisherCambridge University Press

ISBN-10110749902X

ISBN-139781107499027

eBay Product ID (ePID)9038597646

Product Key Features

Number of Pages284 Pages

Publication NameHomotopy Theory of (1) -Categories

LanguageEnglish

Publication Year2018

SubjectTopology, Logic

TypeTextbook

AuthorJulia E. Bergner

Subject AreaMathematics

SeriesLondon Mathematical Society Student Texts

FormatTrade Paperback

Dimensions

Item Height0.6 in

Item Weight14.5 Oz

Item Length9 in

Item Width5.9 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN2018-285687

Reviews'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

TitleLeadingThe

Dewey Edition23

Series Volume NumberSeries Number 90

IllustratedYes

Dewey Decimal514.24

Table Of ContentPreface; 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.

SynopsisHomotopical 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., 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.

LC Classification NumberQA612.7