BirgitRichter
From Categories to Homotopy Theory
From Categories to Homotopy Theory
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Excellent- More about From Categories to Homotopy Theory
Category theory is a fundamental mathematical structure that provides a framework for understanding and applying various areas of mathematics, such as homotopy theory, algebraic topology, and algebra. This book bridges the gap between pure category theory and its applications, making it accessible to graduate students and researchers with a background in algebraic topology and algebra. It introduces category theory with basic definitions and concepts, followed by advanced topics and concrete examples and exercises. Part II covers important applications of category theory, including simplicial objects, diagram categories, and iterated loop spaces.
\n Format: Hardback
\n Length: 400 pages
\n Publication date: 16 April 2020
\n Publisher: Cambridge University Press
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Category theory is a fundamental concept in modern mathematics that provides a structured framework for understanding the mathematical world. It is widely applicable across various fields, including homotopy theory, algebraic topology, and algebra. This book aims to bridge the gap between pure category theory and its numerous applications, making it accessible to graduate students and researchers with a background in algebraic topology and algebra.
The reader is first introduced to category theory, starting with basic definitions and concepts. These foundational elements are then built upon to explore more advanced topics, such as colimits, constructions like the Day convolution product, and the notion of simplicial objects. Part II of the book focuses on important applications of category theory, providing a comprehensive introduction to simplicial objects. This includes an account of quasi-categories and Segal sets, which are essential tools in the study of homotopy theory.
Diagram categories play a central role throughout the book, providing models for iterated loop spaces and contributing to the study of functor homology and homology of small categories. By utilizing the power of category theory, the author demonstrates how it can be used to solve complex problems and advance our understanding of mathematics.
This book is an invaluable resource for anyone interested in exploring the world of category theory and its applications. It offers a clear and comprehensive introduction to the subject, with concrete examples and exercises to help the reader grasp the concepts. Whether you are a graduate student or a researcher in mathematics, this book will provide you with the necessary background information and tools to excel in your field.
\n Weight: 682g\n
Dimension: 159 x 235 x 29 (mm)\n
ISBN-13: 9781108479622\n \n
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