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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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Homotopy Theory of Higher Categories

physics and category theory. In this highly readable book, Carlos Simpson develops a full set of homotopical algebra techniques and proposes a;

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Methods of Homological Algebra

presents basic concepts and results of homotopical algebra. This second edition contains numerous corrections.;

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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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Higher Operads, Higher Categories

Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It;

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More Concise Algebraic Topology

the theory of model categories, which is the central organizing framework for homotopical algebra in general. Examples from topology and;

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Categorification in Geometry, Topology, and Physics

in link homology, interactions between higher representation theory and gauge theory, and double affine Hecke algebra approaches to link homology;

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Building Bridges Between Algebra and Topology

concepts in commutative algebra. Moreover, they also include a higher categories view of Hall algebras and an introduction to the use of idempotent;

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Homotopical Quantum Field Theory

This book provides a general and powerful definition of homotopy algebraic quantum field theory and homotopy prefactorization algebra using;

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Knot Invariants and Higher Representation Theory

these invariants coincide with previous invariants defined by Khovanov for $mathfrak{sl}_2$ and $mathfrak{sl}_3$ and by Mazorchuk-Stroppel and;

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Introduction to Categories, Homological Algebra and Sheaf Cohomology

Categories, homological algebra, sheaves and their cohomology furnish useful methods for attacking problems in a variety of mathematical;

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Categorical Homotopy Theory

unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are;

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Algebras, Quivers and Representations

geometry, cluster algebra theory, commutative algebra, dynamical systems and triangulated categories. In addition, it includes contributions on;

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Locally Presentable and Accessible Categories

universal algebra, model theory, logic and computer science. The aim of this book is to provide an exposition of both the theory and the;

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Categories and Sheaves

Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and;

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Algebraic Operads

of permutations; and operadic Groebner bases, important for applications to algebraic topology, and homological and homotopical algebra. The last;

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Exercises in Algebra

This book is a collection of exercises for courses in higher algebra, linear algebra and geometry. It is helpful for postgraduate students;

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Algebraic Theories

introduction to algebra based on algebraic theories that is accessible to both graduate students and researchers. It will facilitate interactions;

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Algebra and Applications 1

structures, geometric structures on 3-Lie algebras and derived categories are all explored. Algebra and Applications 1 is of great interest to;

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Encyclopedia of Mathematics and its Applications Handbook of Categorical Algebra

with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and;

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Handbook Of Categorical Algebra

with the material in the first, introduces important classes of categories that have played a fundamental role in the subject's development and;

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Higher Algebra

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Higher Algebra for Schools

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Derived Categories

and Verdier in the 1960s. This book is the first in-depth treatment of this important component of homological algebra. It carefully explains;

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Higher algebra

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Higher Topos Theory (AM-170)

Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory;

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Sets for Mathematics

physically common phenomena and advancing to a precise specification of the nature of Categories of Sets. Set theory as the algebra of mappings;

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