Author: Nathan Michael WodarzPublisher:
ISBN:
Category :
Languages : en
Pages : 252
Book Description
The Structure of Endofunctors of the Category of CW-complexes
Author: Nathan Michael WodarzPublisher:
ISBN:
Category :
Languages : en
Pages : 252
Book Description
Category Theory in Context
Author: Emily RiehlPublisher: Courier Dover Publications
ISBN: 0486820807
Category : Mathematics
Languages : en
Pages : 273
Book Description
Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.
Categorical Homotopy Theory
Author: Emily RiehlPublisher: Cambridge University Press
ISBN: 1139952633
Category : Mathematics
Languages : en
Pages : 371
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.
From Categories to Homotopy Theory
Author: Birgit RichterPublisher: Cambridge University Press
ISBN: 1108847625
Category : Mathematics
Languages : en
Pages : 402
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.
Simplicial Structures in Topology
Author: Davide L. FerrarioPublisher: Springer Science & Business Media
ISBN: 1441972366
Category : Mathematics
Languages : en
Pages : 254
Book Description
Simplicial Structures in Topology provides a clear and comprehensive introduction to the subject. Ideas are developed in the first four chapters. The fifth chapter studies closed surfaces and gives their classification. The last chapter of the book is devoted to homotopy groups, which are used in short introduction on obstruction theory. The text is more in tune with the original development of algebraic topology as given by Henry Poincaré (singular homology is discussed). Illustrative examples throughout and extensive exercises at the end of each chapter for practice enhance the text. Advanced undergraduate and beginning graduate students will benefit from this book. Researchers and professionals interested in topology and applications of mathematics will also find this book useful.
Proper Equivariant Stable Homotopy Theory
Author: Dieter DegrijsePublisher: American Mathematical Society
ISBN: 1470467046
Category : Mathematics
Languages : en
Pages : 154
Book Description
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Model Categories
Author: Mark HoveyPublisher: American Mathematical Soc.
ISBN: 0821843613
Category : Mathematics
Languages : en
Pages : 229
Book Description
Model categories are used as a tool for inverting certain maps in a category in a controllable manner. They are useful in diverse areas of mathematics. This book offers a comprehensive study of the relationship between a model category and its homotopy category. It develops the theory of model categories, giving a development of the main examples.
Basic Concepts of Enriched Category Theory
Author: Gregory Maxwell KellyPublisher: CUP Archive
ISBN: 9780521287029
Category : Mathematics
Languages : en
Pages : 260
Book Description
Dissertation Abstracts International
Author: Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 652
Book Description
Author: