1# Library to Find Best eBook for Read
Author : Brandon Doherty
Release : 2024-06-07
Genre : Mathematics
Kind : eBook
Book Rating : 948/5 ( reviews)
Book Synopsis Cubical Models of $(infty ,1)$-Categories by : Brandon Doherty
Download or read book Cubical Models of $(infty ,1)$-Categories written by Brandon Doherty. This book was released on 2024-06-07. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Author : Tom Leinster
Release : 2004-07-22
Genre : Mathematics
Kind : eBook
Book Rating : 159/5 ( reviews)
Book Synopsis Higher Operads, Higher Categories by : Tom Leinster
Download or read book Higher Operads, Higher Categories written by Tom Leinster. This book was released on 2004-07-22. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of higher dimensional category theory for graduate students and researchers in mathematics and mathematical physics.
Author : Birgit Richter
Release : 2020-04-16
Genre : Mathematics
Kind : eBook
Book Rating : 625/5 ( reviews)
Book Synopsis From Categories to Homotopy Theory by : Birgit Richter
Download or read book From Categories to Homotopy Theory written by Birgit Richter. This book was released on 2020-04-16. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Ronald Brown
Release : 2011
Genre : Algebraic topology
Kind : eBook
Book Rating : 838/5 ( reviews)
Book Synopsis Nonabelian Algebraic Topology by : Ronald Brown
Download or read book Nonabelian Algebraic Topology written by Ronald Brown. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: The main theme of this book is that the use of filtered spaces rather than just topological spaces allows the development of basic algebraic topology in terms of higher homotopy groupoids; these algebraic structures better reflect the geometry of subdivision and composition than those commonly in use. Exploration of these uses of higher dimensional versions of groupoids has been largely the work of the first two authors since the mid 1960s. The structure of the book is intended to make it useful to a wide class of students and researchers for learning and evaluating these methods, primarily in algebraic topology but also in higher category theory and its applications in analogous areas of mathematics, physics, and computer science. Part I explains the intuitions and theory in dimensions 1 and 2, with many figures and diagrams, and a detailed account of the theory of crossed modules. Part II develops the applications of crossed complexes. The engine driving these applications is the work of Part III on cubical $\omega$-groupoids, their relations to crossed complexes, and their homotopically defined examples for filtered spaces. Part III also includes a chapter suggesting further directions and problems, and three appendices give accounts of some relevant aspects of category theory. Endnotes for each chapter give further history and references.
Author : Julia E. Bergner
Release : 2018-03-15
Genre : Mathematics
Kind : eBook
Book Rating : 042/5 ( reviews)
Book Synopsis The Homotopy Theory of (∞,1)-Categories by : Julia E. Bergner
Download or read book The Homotopy Theory of (∞,1)-Categories written by Julia E. Bergner. This book was released on 2018-03-15. Available in PDF, EPUB and Kindle. Book excerpt: The notion of an (∞,1)-category has become widely used in homotopy theory, category theory, and in a number of applications. There are many different approaches to this structure, all of them equivalent, and each with its corresponding homotopy theory. This book provides a relatively self-contained source of the definitions of the different models, the model structure (homotopy theory) of each, and the equivalences between the models. While most of the current literature focusses on how to extend category theory in this context, and centers in particular on the quasi-category model, this book offers a balanced treatment of the appropriate model structures for simplicial categories, Segal categories, complete Segal spaces, quasi-categories, and relative categories, all from a homotopy-theoretic perspective. Introductory chapters provide background in both homotopy and category theory and contain many references to the literature, thus making the book accessible to graduates and to researchers in related areas.
