Abstract Homotopy And Simple Homotopy Theory
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Abstract Homotopy And Simple Homotopy Theory
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Author : K Heiner Kamps
language : en
Publisher: World Scientific
Release Date : 1997-04-11
Abstract Homotopy And Simple Homotopy Theory written by K Heiner Kamps and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-04-11 with Mathematics categories.
The abstract homotopy theory is based on the observation that analogues of much of the topological homotopy theory and simple homotopy theory exist in many other categories (e.g. spaces over a fixed base, groupoids, chain complexes, module categories). Studying categorical versions of homotopy structure, such as cylinders and path space constructions, enables not only a unified development of many examples of known homotopy theories but also reveals the inner working of the classical spatial theory. This demonstrates the logical interdependence of properties (in particular the existence of certain Kan fillers in associated cubical sets) and results (Puppe sequences, Vogt's Iemma, Dold's theorem on fibre homotopy equivalences, and homotopy coherence theory).
Abstract Homotopy And Simple Homotopy Theory
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Author : K. H. Kamps
language : en
Publisher:
Release Date : 1986
Abstract Homotopy And Simple Homotopy Theory written by K. H. Kamps and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
Abstract Homotopy And Simple Homotopy Theory
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Author : Klaus Heiner Kamps
language : en
Publisher: World Scientific
Release Date : 1997
Abstract Homotopy And Simple Homotopy Theory written by Klaus Heiner Kamps and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
"This book provides a thorough and well-written guide to abstract homotopy theory. It could well serve as a graduate text in this topic, or could be studied independently by someone with a background in basic algebra, topology, and category theory."
Relation Between Abstract Homotopy And Geometric Homotopy
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Author : Sadanand Verma
language : en
Publisher:
Release Date : 1959
Relation Between Abstract Homotopy And Geometric Homotopy written by Sadanand Verma and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959 with Homotopy theory categories.
A Course In Simple Homotopy Theory
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Author : Marshall M. Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 1973
A Course In Simple Homotopy Theory written by Marshall M. Cohen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Mathematics categories.
Abstract Homotopy Theory
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Author : S. S. Koh
language : en
Publisher:
Release Date : 1960
Abstract Homotopy Theory written by S. S. Koh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Homotopy theory categories.
Controlled Simple Homotopy Theory And Applications
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Author : T. A. Chapman
language : en
Publisher:
Release Date : 2014-09-01
Controlled Simple Homotopy Theory And Applications written by T. A. Chapman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
The Homotopy Theory Of 1 Categories
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Author : Julia E. Bergner
language : en
Publisher: Cambridge University Press
Release Date : 2018-03-15
The Homotopy Theory Of 1 Categories written by Julia E. Bergner and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-15 with Mathematics categories.
An introductory treatment to the homotopy theory of homotopical categories, presenting several models and comparisons between them.
Controlled Simple Homotopy Theory And Applications
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Author : Thomas A. Chapman
language : en
Publisher: Springer
Release Date : 1983
Controlled Simple Homotopy Theory And Applications written by Thomas A. Chapman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Homotopy theory categories.
Simplicial Homotopy Theory
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Author : Paul G. Goerss
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Simplicial Homotopy Theory written by Paul G. Goerss and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.