This book is an introduction to a functorial model theory based on infinitary language categories. The author introduces the properties and foundation of these categories before developing a model theory for functors starting with a countable fragment of an infinitary language. He also presents a new technique for generating generic models with categories by inventing infinite language categories and functorial model theory. In addition, the book covers string models, limit models, and functorial models.
Автор: Joseph Bernstein; Valery Lunts Название: Equivariant Sheaves and Functors ISBN: 3540580719 ISBN-13(EAN): 9783540580713 Издательство: Springer Рейтинг: Цена: 23250.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Introducing the equivariant derived category of sheaves, this monograph also provides applications to the equivariant intersection cohomology. This theory should benefit specialists in representation theory, algebraic geometry or topology.
Автор: Benoit Fresse Название: Homotopy of Operads and Grothendieck-Teichmuller Groups: Part 1: The Algebraic Theory and its Topological Background ISBN: 1470434814 ISBN-13(EAN): 9781470434816 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 107850.00 T Наличие на складе: Невозможна поставка. Описание: The Grothendieck-Teichmuller group was defined by Drinfeld in quantum group theory with insights coming from the Grothendieck program in Galois theory. The ultimate goal of this book is to explain that this group has a topological interpretation as a group of homotopy automorphisms associated to the operad of little 2-discs, which is an object used to model commutative homotopy structures in topology. This volume gives a comprehensive survey on the algebraic aspects of this subject. The book explains the definition of an operad in a general context, reviews the definition of the little discs operads, and explains the definition of the Grothendieck-Teichmuller group from the viewpoint of the theory of operads. In the course of this study, the relationship between the little discs operads and the definition of universal operations associated to braided monoidal category structures is explained. Also provided is a comprehensive and self-contained survey of the applications of Hopf algebras to the definition of a rationalization process, the Malcev completion, for groups and groupoids. Most definitions are carefully reviewed in the book; it requires minimal prerequisites to be accessible to a broad readership of graduate students and researchers interested in the applications of operads.
Автор: Bai Chengming Et Al Название: Operads And Universal Algebra - Proceedings Of The International Conference ISBN: 9814365114 ISBN-13(EAN): 9789814365116 Издательство: World Scientific Publishing Рейтинг: Цена: 111930.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Exemplifies the developments in operad theory, in universal algebra and related topics in algebraic topology and theoretical physics.
Автор: Bremner Название: Algebraic Operads ISBN: 1482248565 ISBN-13(EAN): 9781482248562 Издательство: Taylor&Francis Рейтинг: Цена: 132710.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание:
Algebraic Operads: An Algorithmic Companion presents a systematic treatment of Gr bner bases in several contexts. The book builds up to the theory of Gr bner bases for operads due to the second author and Khoroshkin as well as various applications of the corresponding diamond lemmas in algebra.
The authors present a variety of topics including: noncommutative Gr bner bases and their applications to the construction of universal enveloping algebras; Gr bner bases for shuffle algebras which can be used to solve questions about combinatorics of permutations; and operadic Gr bner bases, important for applications to algebraic topology, and homological and homotopical algebra.
The last chapters of the book combine classical commutative Gr bner bases with operadic ones to approach some classification problems for operads. Throughout the book, both the mathematical theory and computational methods are emphasized and numerous algorithms, examples, and exercises are provided to clarify and illustrate the concrete meaning of abstract theory.
Автор: Jean-Louis Loday; Bruno Vallette Название: Algebraic Operads ISBN: 3642448356 ISBN-13(EAN): 9783642448355 Издательство: Springer Рейтинг: Цена: 102440.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Preface.- 1.Algebras, coalgebras, homology.- 2.Twisting morphisms.- 3.Koszul duality for associative algebras.- 4.Methods to prove Koszulity of an algebra.- 5.Algebraic operad.- 6 Operadic homological algebra.- 7.Koszul duality of operads.- 8.Methods to prove Koszulity of an operad.- 9.The operads As and A\infty.- 10.Homotopy operadic algebras.- 11.Bar and cobar construction of an algebra over an operad.- 12.(Co)homology of algebras over an operad.- 13.Examples of algebraic operads.- Apendices: A.The symmetric group.- B.Categories.- C.Trees.- References.- Index.- List of Notation.
Автор: Benoit Fresse Название: Homotopy of Operads and Grothendieck-Teichmuller Groups: Part 2: The Applications of (Rational) Homotopy Theory Methods ISBN: 1470434822 ISBN-13(EAN): 9781470434823 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 107850.00 T Наличие на складе: Невозможна поставка. Описание: The ultimate goal of this book is to explain that the Grothendieck-Teichmuller group, as defined by Drinfeld in quantum group theory, has a topological interpretation as a group of homotopy automorphisms associated to the little 2-disc operad. To establish this result, the applications of methods of algebraic topology to operads must be developed. This volume is devoted primarily to this subject, with the main objective of developing a rational homotopy theory for operads. The book starts with a comprehensive review of the general theory of model categories and of general methods of homotopy theory. The definition of the Sullivan model for the rational homotopy of spaces is revisited, and the definition of models for the rational homotopy of operads is then explained. The applications of spectral sequence methods to compute homotopy automorphism spaces associated to operads are also explained. This approach is used to get a topological interpretation of the Grothendieck-Teichmuller group in the case of the little 2-disc operad. This volume is intended for graduate students and researchers interested in the applications of homotopy theory methods in operad theory. It is accessible to readers with a minimal background in classical algebraic topology and operad theory.
Автор: Igor V. Nikolaev Название: Noncommutative Geometry: A Functorial Approach ISBN: 3110543176 ISBN-13(EAN): 9783110543179 Издательство: Walter de Gruyter Цена: 123910.00 T Наличие на складе: Невозможна поставка. Описание:
This book covers the basics of noncommutative geometry (NCG) and its applications in topology, algebraic geometry, and number theory. The author takes up the practical side of NCG and its value for other areas of mathematics. A brief survey of the main parts of NCG with historical remarks, bibliography, and a list of exercises is included. The presentation is intended for graduate students and researchers with interests in NCG, but will also serve nonexperts in the field.
Contents Part I: Basics Model examples Categories and functors C∗-algebras
Part II: Noncommutative invariants Topology Algebraic geometry Number theory Part III: Brief survey of NCG Finite geometries Continuous geometries Connes geometries Index theory Jones polynomials Quantum groups Noncommutative algebraic geometry Trends in noncommutative geometry
Автор: Franjou Vincent Название: Lectures on Functor Homology ISBN: 3319213040 ISBN-13(EAN): 9783319213040 Издательство: Springer Рейтинг: Цена: 65210.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role.
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