Homotopy theory of higher categories
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Homotopy theory of higher categories by Carlos Simpson

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Published by Cambridge University Press in Cambridge, New York .
Written in English

Subjects:

  • MATHEMATICS / Topology,
  • Categories (Mathematics),
  • Homotopy theory

Book details:

Edition Notes

Includes bibliographical references (p. [618]-629) and index.

StatementCarlos Simpson
SeriesNew mathematical monographs -- 19, New mathematical monographs -- 19.
Classifications
LC ClassificationsQA612.7 .S56 2012
The Physical Object
Paginationxviii, 634 p. :
Number of Pages634
ID Numbers
Open LibraryOL25263965M
ISBN 100521516951
ISBN 109780521516952
LC Control Number2011026520
OCLC/WorldCa743431958

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Homotopy Type Theory: Univalent Foundations of Mathematics The Univalent Foundations Program Institute for Advanced Study Buy a hardcover copy for $ [ pages, 6" × 9" size, hardcover] Buy a paperback copy for $ [ pages, 6" × 9" size, paperback] Download PDF for on-screen viewing. [+ pages, letter size, in color, with color links]. The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a working theory of higher by: 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 Cited by: 3. First of all, in case anyone missed it, Chris Kapulkin recently wrote a guest post at the n-category cafe summarizing the current state of the art regarding “homotopy type theory as the internal language of higher categories”.

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Again he did not want to find find alternative models as such (see David's excellent reply below), but rather to search for the higher dimensional analogues of Covering Space theory, and to look for a good model of n-categories that would do the job. $\endgroup$ – .   This brings us to the main purpose of the book under review: The homotopy theory of higher categories. Higher dimensional categories are generalizations of the notion of category. A 0-category is a set and an (n+1)-category is a category enriched over an n-category, where enriching means that the Homs are objects of an n-category. A book published on Decem by Chapman and Hall/CRC (ISBN ), pages. Haynes Miller (ed.) Handbook of Homotopy Theory (table of contents) on homotopy theory, including higher algebra and higher category theory. Terminology. The editor, Haynes Miller, comments in the introduction on the choice of title.   Addeddate External-identifier urn:arXiv Identifier arxiv Identifier-ark ark://tc0m Ocr ABBYY FineReader