Read Books Online and Download eBooks, EPub, PDF, Mobi, Kindle, Text Full Free.
Download Three Models For The Homotopy Theory Of Homotopy Theories full books in PDF, epub, and Kindle. Read online Three Models For The Homotopy Theory Of Homotopy Theories ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Author : Julia Elizabeth Bergner
Publisher :
ISBN 13 :
Total Pages : 156 pages
Book Rating : 4.:/5 (712 download)
Download or read book Three Models for the Homotopy Theory of Homotopy Theories written by Julia Elizabeth Bergner and published by . This book was released on 2005 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Marc Aubry
Publisher : Birkhäuser
ISBN 13 : 3034890869
Total Pages : 128 pages
Book Rating : 4.0/5 (348 download)
Download or read book Homotopy Theory and Models written by Marc Aubry and published by Birkhäuser. This book was released on 2012-12-06 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: In keeping with the general aim of the "D.M.V.-Seminar" series, this book is princi pally a report on a group of lectures held at Blaubeuren by Professors H. J. Baues, S. Halperin and J.-M. Lemaire, from October 30 to November 7, 1988. These lec tures were devoted to providing an introduction to the theory of models in algebraic homotopy. The three lecturers acted in concert to produce a coherent exposition of the theory. Commencing from a common starting point, each of them then proceeded naturally to his own subject of research. The reader who is already familiar with their scientific work will certainly give the lecturers their due. Having been asked by the speakers to take on the responsibility of writing down the notes, it seemed to me that the material elucidated in the short span of fifteen hours was too dense to appear, unedited, in book form. Some amplification was necessary. Of course I submitted to them the final version of this book, which received their approval. I thank them for this token of confidence. I am also grateful to all three for their help and advice in writing this book. I am particularly indebted to J.-M. Lemaire who was indeed very often consulted. For basic notions (in particular those concerning homotopy groups, CW complexes, (co)homology and homological algebra) the reader is advised to refer to the fundamental books written by E. H. Spanier [47], R. M. Switzer [49] and G. Whitehead [52].
Author : Julia E. Bergner
Publisher : Cambridge University Press
ISBN 13 : 1107101360
Total Pages : 289 pages
Book Rating : 4.1/5 (71 download)
Download or read book The Homotopy Theory of (?,1)-Categories written by Julia E. Bergner and published by Cambridge University Press. This book was released on 2018-03-15 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory treatment to the homotopy theory of homotopical categories, presenting several models and comparisons between them.
Author : Marc Aubry
Publisher :
ISBN 13 : 9783034890878
Total Pages : 132 pages
Book Rating : 4.8/5 (98 download)
Download or read book Homotopy Theory and Models written by Marc Aubry and published by . This book was released on 1995-03-27 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based upon notes taken by the author at the DMV Seminar on Algebraic Models of Homotopy Types led by H.J. Baues, S. Halperin and J.-M. Lemaire in 1988. The notes have been substantially reorganized and expanded for this publication and now include some additional important proofs. The aim of the work is to provide an overview of homotopy theory from the point of view of algebraic models of homotopy types, leading the reader from the basic definitions in algebraic topology to specific fields of research. The exposition is directed towards graduate students as well as researchers from other fields. Due to the scope and size of this book, only a few complete proofs could be given. But the fundamental concepts and methods of the subject are pointed out, and a number of recent results are included together with the essential bibliographic references. The text begins with a review of the basic notions of homotopy theory. An extensive discussion of rational homotopy theory, emphasizing both the Sullivan and the Quillen models, follows. Next, the Adams-Hilton and the Anick models are shown to yield some integral information. The last chapter gives an introduction to the integral classification of homotopy types, along the lines initiated by J.H.C. Whitehead and considerably developed by H. Baues during the last decade.
Author :
Publisher :
ISBN 13 :
Total Pages : 100 pages
Book Rating : 4.:/5 (931 download)
Download or read book Two Models for the Homotopy Theory of Cocomplete Homotopy Theories written by and published by . This book was released on 2014 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : William G. Dwyer
Publisher : American Mathematical Soc.
ISBN 13 : 0821839756
Total Pages : 194 pages
Book Rating : 4.8/5 (218 download)
Download or read book Homotopy Limit Functors on Model Categories and Homotopical Categories written by William G. Dwyer and published by American Mathematical Soc.. This book was released on 2004 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this monograph, which is aimed at the graduate level and beyond, is to obtain a deeper understanding of Quillen's model categories. A model category is a category together with three distinguished classes of maps, called weak equivalences, cofibrations, and fibrations. Model categories have become a standard tool in algebraic topology and homological algebra and, increasingly, in other fields where homotopy theoretic ideas are becoming important, such as algebraic $K$-theory and algebraic geometry. The authors' approach is to define the notion of a homotopical category, which is more general than that of a model category, and to consider model categories as special cases of this. A homotopical category is a category with only a single distinguished class of maps, called weak equivalences, subject to an appropriate axiom. This enables one to define ``homotopical'' versions of such basic categorical notions as initial and terminal objects, colimit and limit functors, cocompleteness and completeness, adjunctions, Kan extensions, and universal properties. There are two essentially self-contained parts, and part II logically precedes part I. Part II defines and develops the notion of a homotopical category and can be considered as the beginnings of a kind of ``relative'' category theory. The results of part II are used in part I to obtain a deeper understanding of model categories. The authors show in particular that model categories are homotopically cocomplete and complete in a sense stronger than just the requirement of the existence of small homotopy colimit and limit functors. A reader of part II is assumed to have only some familiarity with the above-mentioned categorical notions. Those who read part I, and especially its introductory chapter, should also know something about model categories.
Author : Haynes Miller
Publisher : CRC Press
ISBN 13 : 1351251619
Total Pages : 982 pages
Book Rating : 4.3/5 (512 download)
Download or read book Handbook of Homotopy Theory written by Haynes Miller and published by CRC Press. This book was released on 2020-01-23 with total page 982 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.
Author : Philip S. Hirschhorn
Publisher : American Mathematical Soc.
ISBN 13 : 0821849174
Total Pages : 482 pages
Book Rating : 4.8/5 (218 download)
Download or read book Model Categories and Their Localizations written by Philip S. Hirschhorn and published by American Mathematical Soc.. This book was released on 2003 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to explain modern homotopy theory in a manner accessible to graduate students yet structured so that experts can skip over numerous linear developments to quickly reach the topics of their interest. Homotopy theory arises from choosing a class of maps, called weak equivalences, and then passing to the homotopy category by localizing with respect to the weak equivalences, i.e., by creating a new category in which the weak equivalences are isomorphisms. Quillen defined a model category to be a category together with a class of weak equivalences and additional structure useful for describing the homotopy category in terms of the original category. This allows you to make constructions analogous to those used to study the homotopy theory of topological spaces. A model category has a class of maps called weak equivalences plus two other classes of maps, called cofibrations and fibrations. Quillen's axioms ensure that the homotopy category exists and that the cofibrations and fibrations have extension and lifting properties similar to those of cofibration and fibration maps of topological spaces. During the past several decades the language of model categories has become standard in many areas of algebraic topology, and it is increasingly being used in other fields where homotopy theoretic ideas are becoming important, including modern algebraic $K$-theory and algebraic geometry. All these subjects and more are discussed in the book, beginning with the basic definitions and giving complete arguments in order to make the motivations and proofs accessible to the novice. The book is intended for graduate students and research mathematicians working in homotopy theory and related areas.
Author : Benoit Fresse
Publisher : American Mathematical Soc.
ISBN 13 : 1470434822
Total Pages : 743 pages
Book Rating : 4.4/5 (74 download)
Download or read book Homotopy of Operads and Grothendieck-Teichmuller Groups written by Benoit Fresse and published by American Mathematical Soc.. This book was released on 2017-05-22 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ultimate goal of this book is to explain that the Grothendieck–Teichmüller group, as defined by Drinfeld in quantum group theory, has a topological interpretation as a group of homotopy automorphisms associated to the little 2-disc operad. To establish this result, the applications of methods of algebraic topology to operads must be developed. This volume is devoted primarily to this subject, with the main objective of developing a rational homotopy theory for operads. The book starts with a comprehensive review of the general theory of model categories and of general methods of homotopy theory. The definition of the Sullivan model for the rational homotopy of spaces is revisited, and the definition of models for the rational homotopy of operads is then explained. The applications of spectral sequence methods to compute homotopy automorphism spaces associated to operads are also explained. This approach is used to get a topological interpretation of the Grothendieck–Teichmüller group in the case of the little 2-disc operad. This volume is intended for graduate students and researchers interested in the applications of homotopy theory methods in operad theory. It is accessible to readers with a minimal background in classical algebraic topology and operad theory.
Author : Paul G. Goerss
Publisher : Birkhäuser
ISBN 13 : 3034887078
Total Pages : 520 pages
Book Rating : 4.0/5 (348 download)
Download or read book Simplicial Homotopy Theory written by Paul G. Goerss and published by Birkhäuser. This book was released on 2012-12-06 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, including algebraic K-theory. This book supplies a modern exposition of these ideas, emphasizing model category theoretical techniques. Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups, Postnikov towers, and bisimplicial sets. The more advanced material includes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence. Interspersed throughout are many results and ideas well-known to experts, but uncollected in the literature. Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed.
Author : Brian A. Munson
Publisher : Cambridge University Press
ISBN 13 : 1107030250
Total Pages : 649 pages
Book Rating : 4.1/5 (7 download)
Download or read book Cubical Homotopy Theory written by Brian A. Munson and published by Cambridge University Press. This book was released on 2015-10-06 with total page 649 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern, example-driven introduction to cubical diagrams and related topics such as homotopy limits and cosimplicial spaces.
Author : Carlos Simpson
Publisher : Cambridge University Press
ISBN 13 : 1139502190
Total Pages : 653 pages
Book Rating : 4.1/5 (395 download)
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.
Author : Mark Hovey
Publisher : American Mathematical Society(RI)
ISBN 13 : 9780821813591
Total Pages : 0 pages
Book Rating : 4.8/5 (135 download)
Download or read book Model Categories written by Mark Hovey and published by American Mathematical Society(RI). This book was released on 1999 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A study of the relationship between a model category and its homotopy category. Develops the theory of model categories, giving a careful treatment of the main examples, and highlights the proof within the theory that the homotopy category of any model category is naturally a closed module over the homotopy category of simplicial sets. This leads to a generalization of the loop and suspension functions in the homotopy category of a pointed model category, and then to discussion of the stable case. Includes a chapter of problems. For graduate students with background in category and set theories. Annotation copyrighted by Book News, Inc., Portland, OR.
Author : Stefan Schwede
Publisher : Cambridge University Press
ISBN 13 : 110842581X
Total Pages : 847 pages
Book Rating : 4.1/5 (84 download)
Download or read book Global Homotopy Theory written by Stefan Schwede and published by Cambridge University Press. This book was released on 2018-09-06 with total page 847 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, self-contained approach to global equivariant homotopy theory, with many detailed examples and sample calculations.
Author : Scott Balchin
Publisher : Springer Nature
ISBN 13 : 3030750353
Total Pages : 326 pages
Book Rating : 4.0/5 (37 download)
Download or read book A Handbook of Model Categories written by Scott Balchin and published by Springer Nature. This book was released on 2021-10-29 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book outlines a vast array of techniques and methods regarding model categories, without focussing on the intricacies of the proofs. Quillen model categories are a fundamental tool for the understanding of homotopy theory. While many introductions to model categories fall back on the same handful of canonical examples, the present book highlights a large, self-contained collection of other examples which appear throughout the literature. In particular, it collects a highly scattered literature into a single volume. The book is aimed at anyone who uses, or is interested in using, model categories to study homotopy theory. It is written in such a way that it can be used as a reference guide for those who are already experts in the field. However, it can also be used as an introduction to the theory for novices.
Author : John C. Baez
Publisher : Springer Science & Business Media
ISBN 13 : 1441915362
Total Pages : 292 pages
Book Rating : 4.4/5 (419 download)
Download or read book Towards Higher Categories written by John C. Baez and published by Springer Science & Business Media. This book was released on 2009-09-24 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 itself. It begins with a paper by John Baez and Michael Shulman which explores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory. The idea is to give some of the motivations behind this subject. There are then two survey articles, by Julie Bergner and Simona Paoli, about (infinity,1) categories and about the algebraic modelling of homotopy n-types. These are areas that are particularly well understood, and where a fully integrated theory exists. The main focus of the book is on the richness to be found in the theory of bicategories, which gives the essential starting point towards the understanding of higher categorical structures. An article by Stephen Lack gives a thorough, but informal, guide to this theory. A paper by Larry Breen on the theory of gerbes shows how such categorical structures appear in differential geometry. This book is dedicated to Max Kelly, the founder of the Australian school of category theory, and an historical paper by Ross Street describes its development.
Author :
Publisher : Academic Press
ISBN 13 : 0080873804
Total Pages : 383 pages
Book Rating : 4.0/5 (88 download)
Download or read book Homotopy Theory: An Introduction to Algebraic Topology written by and published by Academic Press. This book was released on 1975-11-12 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homotopy Theory: An Introduction to Algebraic Topology
