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The Homotopy Theory of ( ,1)-Categories

different approaches to this structure, all of them equivalent, and each with its corresponding homotopy theory. This book provides a relatively;

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The Homotopy Theory of ( ,1)-Categories

different approaches to this structure, all of them equivalent, and each with its corresponding homotopy theory. This book provides a relatively;

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Categorical Homotopy Theory

This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two;

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Foundations of Stable Homotopy Theory

and decades. There is much folklore but very few easy entry points. This comprehensive introduction to stable homotopy theory changes that. It;

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Model Categories

category and its homotopy category. The author develops the theory of model categories, giving a careful development of the main examples. One;

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From Categories to Homotopy Theory

bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to;

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Algebraic Homotopy

, including an introduction to rational homotopy theory in terms of both differential Lie algebras and De Rham algebras. The author describes powerful;

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Higher Categories and Homotopical Algebra

This book provides an introduction to modern homotopy theory through the lens of higher categories after Joyal and Lurie, giving access to;

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Cambridge Studies in Advanced Mathematics

, including an introduction to rational homotopy theory in terms of both differential Lie algebras and De Rham algebras. The author describes powerful;

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Homotopy Theory with Bornological Coarse Spaces

Providing a new approach to assembly maps, this book develops the foundations of coarse homotopy using the language of infinity categories;

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Model Categories And Their Localizations

skip over numerous linear developments to quickly reach the topics of their interest. Homotopy theory arises from choosing a class of maps;

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Cubical Homotopy Theory

Graduate students and researchers alike will benefit from this treatment of classical and modern topics in homotopy theory of topological;

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Homotopy of Operads and Grothendieck-Teichmuller Groups: Part 2

of developing a rational homotopy theory for operads. The book starts with a comprehensive review of the general theory of model categories and;

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A Handbook of Model Categories

. Quillen model categories are a fundamental tool for the understanding of homotopy theory. While many introductions to model categories fall back;

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Homotopy Theory

spectra associated to perfectoid fields, and the theory of higher homotopy operations.;

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Representation Theory and Beyond

It presents several themes of contemporary representation theory together with some new tools, such as stable ?-categories, stable;

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Algebraic Methods In Unstable Homotopy Theory

The most modern and thorough treatment of unstable homotopy theory available. The focus is on those methods from algebraic topology which;

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Simplicial Homotopy Theory

homotopy theory from a modern point of view [...] The book is well written. [...] The book can be highly recommended to anybody who wants to learn;

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Calculus of Fractions and Homotopy Theory

The main purpose of the present work is to present to the reader a particularly nice category for the study of homotopy, namely the homo;

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Lectures on Factorization Homology Categories and Topological Field Theories

. Along the way, the reader is also introduced to modern ideas in homotopy theory and category theory, particularly as it relates to the use;

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Homotopy Limit Functors on Model Categories and Homotopical Categories

of relative category theory. The results of part II are used in part I to obtain a deeper understanding of model categories. The authors show;

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Homotopy Theory of Higher Categories

working theory of higher categories. Starting with a cohesive overview of the many different approaches currently used by researchers, the author;

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An Alpine Bouquet of Algebraic Topology

spectra, infinity-categories and Segal spaces, equivariant homotopy theory, algebraic $K$-theory and topological cyclic, periodic, or Hochschild;

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Handbook of Homotopy Theory

The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to;

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Tensor Categories

algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book;

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Advances in Homotopy Theory

contributions to homotopy theory, highlighting problems and initiating new methods. The present volume contains papers from internationally;

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An Introduction to Homotopy Theory

more complex treatment to be found in original papers. The first six chapters describe the essential ideas of homotopy theory: homotopy groups;

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