2 edition of **Homotopy theory of higher categories** found in the catalog.

Homotopy theory of higher categories

Carlos Simpson

- 66 Want to read
- 15 Currently reading

Published
**2012**
by Cambridge University Press in Cambridge, New York
.

Written in English

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

**Edition Notes**

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

Statement | Carlos Simpson |

Series | New mathematical monographs -- 19, New mathematical monographs -- 19. |

Classifications | |
---|---|

LC Classifications | QA612.7 .S56 2012 |

The Physical Object | |

Pagination | xviii, 634 p. : |

Number of Pages | 634 |

ID Numbers | |

Open Library | OL25263965M |

ISBN 10 | 0521516951 |

ISBN 10 | 9780521516952 |

LC Control Number | 2011026520 |

OCLC/WorldCa | 743431958 |

Categorical Homotopy Theory This book develops abstract homotopy theory from the categorical perspective, with a particular focus on examples. Part I discusses two competing perspectives by which Simpson Homotopy Theory of Higher Categories E. Fricain and J. Mashreghi The Theory of H(b) Spaces I E. John Baez Minicourse at the Calgary summer school on Topics in Homotopy Theory August , Higher Gauge Theory, Homotopy Theory and n-Categories These are rough notes for four lectures on higher gauge theory, aimed at explaining how this theory is related to some classic themes from homotopy theory, such as Eilenberg-Mac Lane spaces.

More Concise Algebraic Topology Localization, completion, and model categories. This book explains the following topics: the fundamental group, covering spaces, ordinary homology and cohomology in its singular, cellular, axiomatic, and represented versions, higher homotopy groups and the Hurewicz theorem, basic homotopy theory including. Submission history From: Carlos T. Simpson [] [via CCSD proxy] [v1] Fri, 22 Jan GMT (kb)Cited by:

complexes of modules over a ring R. The homotopy theory of Top is of course fa-miliar, and it turns out that the homotopy theory ofCh Ris what is usually called homological algebra. Comparing these two examples helps explain why Quillen called the study of model categories \homotopical algebra" and thought of it as a. This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular /5(2).

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Homotopical categories and derived functors 13 Derived functors via deformations 18 Classical derived functors between abelian categories 22 Preview of homotopy limits and colimits 23 Chapter 3. Basic concepts of enriched category theory 25 A ﬁrst example 26 The base for enrichment 26 Enriched categories 27 File Homotopy theory of higher categories book 1MB.

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”.

adshelp[at] The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86ACited by: Get this from a library. Homotopy theory of higher categories. [Carlos Simpson] -- "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. 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 categories.

Starting with a cohesive overview of the many different. Homotopy theory of higher categories Carlos Simpson To cite this version: Carlos Simpson. Homotopy theory of higher categories. Cambridge University Press, 19,New mathematical monographs, hal. 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 One of the major motivations of Homotopy Type Theory is that it naturally builds in higher coherences from the beginning.

One important setting where higher coherence requirements get annoying is higher category theory. It's easy to talk about $\infty$-groupoids in HoTT, they're just types and you build them as higher inductive types. From Categories to Homotopy Theory CHAPTER Simplicial Objects The Simplicial Category n and Higher Categories CHAPTER Functor Homology Tensor Products Tor and Ext models of homotopy colimits and much more.

This book has two parts. The rst one gives an introduction to category theory. Strictly speaking, the theory of categories is not a part of category theory, but of higher category theory [6,53,54, 72].

Grothendieck's homotopy hypothesis [35,56] made higher category theory. HigherCategoriesand HomotopicalAlgebra DENIS-CHARLES CISINSKI between two 1-categories, to see homotopy types (under the form of Kan of the classical homotopy theory of simplicial sets, nor of Quillen’s model ,eventheKan-Quillenmodelcategorystructure,File Size: 1MB.

Local Homotopy Theory - Ebook written by John F. Jardine. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Local Homotopy Theory.

Our plan is to start from Lecture notes on K-theory and Categorical homotopy theory, we hope to get a solid understanding higher algebraic K-theory and categorical homotopy theory by the end of this semester, and probably learn some $\infty$-categories theory.

Meeting time and location: Each Wednesday pm at 4N49 and Friday pm at 4C6. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): portant la référence ANRBLAN (HODAG). This is draft material from a forthcoming book to be published by Cambridge University Press in the New Mathematical Monographs series.

This publication is in copyright. c Carlos T. Simpson v This is the first draft of a book about .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 categories.(This is basically section of the Homotopy Type Theory book, below.) Homotopy Type Theory: A synthetic approach to higher equalities.

Chapter written for the book Categories for the working philosopher (Oxford University Press, ), edited by Elaine Landry. Available on the arXiv: Brouwer's fixed-point theorem in real-cohesive.