Homotopy in Exact Categories PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Homotopy in Exact Categories PDF full book. Access full book title Homotopy in Exact Categories by Jack Kelly. Download full books in PDF and EPUB format.
Author: Jack Kelly
Publisher: American Mathematical Society
ISBN: 1470470411
Category : Mathematics
Languages : en
Pages : 172
Get Book Here
Book Description
View the abstract.
Author: Jack Kelly
Publisher: American Mathematical Society
ISBN: 1470470411
Category : Mathematics
Languages : en
Pages : 172
Get Book Here
Book Description
View the abstract.
Author:
Publisher: Univalent Foundations
ISBN:
Category :
Languages : en
Pages : 484
Get Book Here
Book Description
Author: Emily Riehl
Publisher: Cambridge University Press
ISBN: 1139952633
Category : Mathematics
Languages : en
Pages : 371
Get Book Here
Book Description
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 formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.
Author: J. P. May
Publisher: University of Chicago Press
ISBN: 9780226511832
Category : Mathematics
Languages : en
Pages : 262
Get Book Here
Book Description
Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
Author: Klaus Heiner Kamps
Publisher: World Scientific
ISBN: 9789810216023
Category : Mathematics
Languages : en
Pages : 474
Get Book Here
Book Description
"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."
Author: Birgit Richter
Publisher: Cambridge University Press
ISBN: 1108847625
Category : Mathematics
Languages : en
Pages : 402
Get Book Here
Book Description
Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.
Author: Brian A. Munson
Publisher: Cambridge University Press
ISBN: 1107030250
Category : Mathematics
Languages : en
Pages : 649
Get Book Here
Book Description
A modern, example-driven introduction to cubical diagrams and related topics such as homotopy limits and cosimplicial spaces.
Author: Denis-Charles Cisinski
Publisher: Cambridge University Press
ISBN: 1108473202
Category : Mathematics
Languages : en
Pages : 449
Get Book Here
Book Description
At last, a friendly introduction to modern homotopy theory after Joyal and Lurie, reaching advanced tools and starting from scratch.
Author: Hans J. Baues
Publisher: Cambridge University Press
ISBN: 0521333768
Category : Mathematics
Languages : en
Pages : 490
Get Book Here
Book Description
This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in topology and algebra are discussed, including an introduction to rational homotopy theory in terms of both differential Lie algebras and De Rham algebras. The author describes powerful tools for homotopy classification problems, particularly for the classification of homotopy types and for the computation of the group homotopy equivalences. Applications and examples of such computations are given, including when the fundamental group is non-trivial. Moreover, the deep connection between the homotopy classification problems and the cohomology theory of small categories is demonstrated. The prerequisites of the book are few: elementary topology and algebra. Consequently, this account will be valuable for non-specialists and experts alike. It is an important supplement to the standard presentations of algebraic topology, homotopy theory, category theory and homological algebra.
Author: Julia E. Bergner
Publisher: Cambridge University Press
ISBN: 1107101360
Category : Mathematics
Languages : en
Pages : 289
Get Book Here
Book Description
An introductory treatment to the homotopy theory of homotopical categories, presenting several models and comparisons between them.
