Homotopy Theory of Higher Categories

Homotopy Theory of Higher Categories
Author :
Publisher : Cambridge University Press
Total Pages : 653
Release :
ISBN-10 : 9781139502191
ISBN-13 : 1139502190
Rating : 4/5 (91 Downloads)

Book Synopsis Homotopy Theory of Higher Categories by : Carlos Simpson

Download or read book Homotopy Theory of Higher Categories written by Carlos Simpson and published by Cambridge University Press. This book was released on 2011-10-20 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 approaches currently used by researchers, the author proceeds with a detailed exposition of one of the most widely used techniques: the construction of a Cartesian Quillen model structure for higher categories. The fully iterative construction applies to enrichment over any Cartesian model category, and yields model categories for weakly associative n-categories and Segal n-categories. A corollary is the construction of higher functor categories which fit together to form the (n+1)-category of n-categories. The approach uses Tamsamani's definition based on Segal's ideas, iterated as in Pelissier's thesis using modern techniques due to Barwick, Bergner, Lurie and others.


Homotopy Theory of Higher Categories Related Books

Homotopy Theory of Higher Categories
Language: en
Pages: 653
Authors: Carlos Simpson
Categories: Mathematics
Type: BOOK - Published: 2011-10-20 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

The study of higher categories is attracting growing interest for its many applications in topology, algebraic geometry, mathematical physics and category theor
Towards Higher Categories
Language: en
Pages: 292
Authors: John C. Baez
Categories: Algebra
Type: BOOK - Published: 2009-09-24 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory
Higher Operads, Higher Categories
Language: en
Pages: 451
Authors: Tom Leinster
Categories: Mathematics
Type: BOOK - Published: 2004-07-22 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

Foundations of higher dimensional category theory for graduate students and researchers in mathematics and mathematical physics.
Higher Categories and Homotopical Algebra
Language: en
Pages: 449
Authors: Denis-Charles Cisinski
Categories: Mathematics
Type: BOOK - Published: 2019-05-02 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

At last, a friendly introduction to modern homotopy theory after Joyal and Lurie, reaching advanced tools and starting from scratch.
Categories for the Working Mathematician
Language: en
Pages: 320
Authors: Saunders Mac Lane
Categories: Mathematics
Type: BOOK - Published: 2013-04-17 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural tr