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The Homotopy Theory of ( ,1)-Categories

The notion of an ( ,1)-category has become widely used in homotopy theory, category theory, and in a number of applications. There are many;

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The Homotopy Theory of ( ,1)-Categories

The notion of an ( ,1)-category has become widely used in homotopy theory, category theory, and in a number of applications. There are many;

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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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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

topics such as monoidal structures, localisations and chromatic homotopy theory. The appendix containing essential facts on model categories, the;

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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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Algebraic Homotopy

connection between the homotopy classification problems and the cohomology theory of small categories is demonstrated. The prerequisites of the book;

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Cambridge Studies in Advanced Mathematics

connection between the homotopy classification problems and the cohomology theory of small categories is demonstrated. The prerequisites of the book;

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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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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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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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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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Model Categories And Their Localizations

The aim of this book is to explain modern homotopy theory in a manner accessible to graduate students yet structured so that experts can;

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Cubical Homotopy Theory

I focuses on foundational material on homotopy theory, viewed through the lens of cubical diagrams: fibrations and cofibrations, homotopy;

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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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K-Theory

over algebraic geometry, topology, algebraic $K$-theory and number theory. Algebraic theory, $\\mathbb{A}^1$-homotopy theory and topological $K$-theory;

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Representation Theory and Beyond

theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more;

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Homotopy Theory

This volume contains the proceedings of the conference Homotopy Theory: Tools and Applications, in honor of Paul Goerss's 60th birthday;

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Calculus of Fractions and Homotopy Theory

usual grounding in category theory - summarized in the Dictionary - and the theory of categories of fractions which forms the subject of the;

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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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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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An Introduction to Homotopy Theory

Since the introduction of homotopy groups by Hurewicz in 1935, homotopy theory has occupied a prominent place in the development;

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Simplicial Homotopy Theory

theoretical techniques. Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups, Postnikov;

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Triangulated Categories. (AM-148), Volume 148

The first two chapters of this book offer a modern, self-contained exposition of the elementary theory of triangulated categories and their;

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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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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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Tensor Categories

generalizations of vector spaces-objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes;

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