Tensor Categories and Hopf Algebras, Nicolas Andruskiewitsch, Dmitri Nikshych

Автор: Mac Lane
Название: Categories for the Working Mathematician
ISBN: 0387984038 ISBN-13(EAN): 9780387984032
Издательство: Springer
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Описание: This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.

Автор: Crole
Название: Categories for Types
ISBN: 0521457017 ISBN-13(EAN): 9780521457019
Издательство: Cambridge Academ
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Описание: This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories.

Автор: Pavel Etingof, Shlomo Gelaki, Dmitri Nikshych, Victor Ostrik
Название: Tensor Categories
ISBN: 1470434415 ISBN-13(EAN): 9781470434410
Издательство: Mare Nostrum (Eurospan)
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Описание: Is there a vector space whose dimension is the golden ratio? Of course not-the golden ratio is not an integer! But this can happen for generalizations of vector spaces-objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.

Автор: Alberto Facchini, Lorna Gregory, Sonia L`Innocente, Marcus Tressl
Название: Model Theory of Modules, Algebras and Categories
ISBN: 1470443678 ISBN-13(EAN): 9781470443672
Издательство: Mare Nostrum (Eurospan)
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Цена: 108680.00 T
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Описание: This volume contains the proceedings of the international conference Model Theory of Modules, Algebras and Categories, held from July 28-August 2, 2017, at the Ettore Majorana Foundation and Centre for Scientific Culture in Erice, Italy.Papers contained in this volume cover recent developments in model theory, module theory and category theory, and their intersection.

Автор: Matthew Ballard; Charles Doran; David Favero; Eric
Название: Superschool on Derived Categories and D-branes
ISBN: 3030062708 ISBN-13(EAN): 9783030062705
Издательство: Springer
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Описание: This book consists of a series of introductory lectures on mirror symmetry and its surrounding topics. These lectures were provided by participants in the PIMS Superschool for Derived Categories and D-branes in July 2016. Together, they form a comprehensive introduction to the field that integrates perspectives from mathematicians and physicists alike. These proceedings provide a pleasant and broad introduction into modern research topics surrounding string theory and mirror symmetry that is approachable to readers new to the subjects. These topics include constructions of various mirror pairs, approaches to mirror symmetry, connections to homological algebra, and physical motivations. Of particular interest is the connection between GLSMs, D-branes, birational geometry, and derived categories, which is explained both from a physical and mathematical perspective. The introductory lectures provided herein highlight many features of this emerging field and give concrete connections between the physics and the math.Mathematical readers will come away with a broader perspective on this field and a bit of physical intuition, while physicists will gain an introductory overview of the developing mathematical realization of physical predictions.

Автор: Simona Paoli
Название: Simplicial Methods for Higher Categories
ISBN: 3030056732 ISBN-13(EAN): 9783030056735
Издательство: Springer
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Цена: 130430.00 T
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Описание: This monograph presents a new model of mathematical structures called weak n-categories. These structures find their motivation in a wide range of fields, from algebraic topology to mathematical physics, algebraic geometry and mathematical logic.While strict n-categories are easily defined in terms associative and unital composition operations they are of limited use in applications, which often call for weakened variants of these laws. The author proposes a new approach to this weakening, whose generality arises not from a weakening of such laws but from the very geometric structure of its cells; a geometry dubbed weak globularity. The new model, called weakly globular n-fold categories, is one of the simplest known algebraic structures yielding a model of weak n-categories. The central result is the equivalence of this model to one of the existing models, due to Tamsamani and further studied by Simpson. This theory has intended applications to homotopy theory, mathematical physics and to long-standing open questions in category theory.As the theory is described in elementary terms and the book is largely self-contained, it is accessible to beginning graduate students and to mathematicians from a wide range of disciplines well beyond higher category theory. The new model makes a transparent connection between higher category theory and homotopy theory, rendering it particularly suitable for category theorists and algebraic topologists. Although the results are complex, readers are guided with an intuitive explanation before each concept is introduced, and with diagrams showing the interconnections between the main ideas and results.

Автор: Michael Winter
Название: Goguen Categories
ISBN: 9048175542 ISBN-13(EAN): 9789048175543
Издательство: Springer
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Цена: 139750.00 T
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Описание: Goguen categories extend the relational calculus and its categorical formalization to the fuzzy world. Starting from the fundamental concepts of sets, binary relations and lattices, this book introduces several categorical formulations of an abstract theory of relations such as allegories, Dedekind categories and related structures.

Автор: Eva Gray; Horst Schubert
Название: Categories
ISBN: 3642653669 ISBN-13(EAN): 9783642653667
Издательство: Springer
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Цена: 79190.00 T
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Описание: Categorical methods of speaking and thinking are becoming more and more widespread in mathematics because they achieve a unifi- cation of parts of different mathematical fields; The purpose of this book is to introduce the reader to the central part of category theory and to make the literature accessible to the reader who wishes to go farther.

Автор: John C. Baez; J. Peter May
Название: Towards Higher Categories
ISBN: 1441915230 ISBN-13(EAN): 9781441915238
Издательство: Springer
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Описание: Here is a guide to the theory of higher categorical structures. The main focus of the book is on the richness to be found in the theory of bicategories, which gives the essential starting point towards the understanding of higher categorical structures.

Автор: Frank W. Anderson; Kent R. Fuller
Название: Rings and Categories of Modules
ISBN: 0387978453 ISBN-13(EAN): 9780387978451
Издательство: Springer
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Цена: 65170.00 T
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Описание: Offers an account of much of the theory of rings and modules. This book provides the basic definitions and properties of rings, modules and homomorphisms. It offers comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, and Morita equivalence and duality.

Автор: Ballard
Название: Superschool on Derived Categories and D-branes
ISBN: 3319916254 ISBN-13(EAN): 9783319916255
Издательство: Springer
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Цена: 167700.00 T
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Описание: Abelian and Triangulated Categories (C. Hanratty).- Derived Categories and Derived Functors (N.K. Chidambaram).- Introduction to Quivers (M. Chinen).- Semi-orthogonal Decompositions of Derived Categories (Y. Liu).- Introduction to Bridgeland Stability Conditions (R. Tramel).- A Brief Introduction to Geometric Invariant Theory (N. Grieve).- Birational Geometry and Derived Categories (C. Diemer).- Introduction to Mirror Symmetry (R. Hughes).- Batyrev Mirror Symmetry (M. Talpo).- Differential Graded Categories (A.A. Takeda).- Introduction to Symplectic Geometry and Fukaya Category (A.Z. Zhang).- Homological Mirror Symmetry (A. Harder).- The Syz Conjecture Via Homological Mirror Symmetry (D. Bejleri).- The Derived Category of Coherent Sheaves and B-model Topological String Theory (S. Pietromonaco).- Introduction to Topological String Theories (K. Osuga).- An Overview of B-branes in Gauged Linear Sigma Models (N. Ishtiaque).

Автор: Vladimir Turaev; Alexis Virelizier
Название: Monoidal Categories and Topological Field Theory
ISBN: 3319498339 ISBN-13(EAN): 9783319498331
Издательство: Springer
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Цена: 130430.00 T
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Описание:

This monograph is devoted to monoidal categories and their connections with 3-dimensional topological field theories. Starting with basic definitions, it proceeds to the forefront of current research.