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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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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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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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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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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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Homotopy Theory

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

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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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Representation Theory and Beyond

algebras, and the higher Auslander-Reiten theory studied via homotopy theory.;

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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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Commutator Calculus and Groups of Homotopy Classes

extends results of rational homotopy theory to a subring of the rationale. The methods of proof employ classical commutator calculus of nilpotent;

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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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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

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

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Algebraic Structure of String Field Theory

from the perspective of homotopy algebras and their operadic origin. Part I reviews string field theory from the point of view;

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Building Bridges Between Algebra and Topology

growing area of support theory for triangulated categories to the striking consequences of the formulation in the homotopy theory of classical;

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Triangulated Categories of Mixed Motives

in a self-contained manner and could be accessible to graduate students with a background in algebraic geometry and homotopy theory. It;

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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 L-theory and Topological Manifolds

. The algebraic L-theory assembly map is used to give a purely algebraic formulation of the Novikov conjectures on the homotopy invariance;

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Algebraic L-theory and Topological Manifolds

. The algebraic L-theory assembly map is used to give a purely algebraic formulation of the Novikov conjectures on the homotopy invariance;

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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

. Model categories have become a standard tool in algebraic topology and homological algebra and, increasingly, in other fields where homotopy;

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The K-book

that even working in a purely algebraic context, one requires techniques from homotopy theory to construct the higher $K$-groups and to perform;

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