Superschool on Derived Categories and D-branes, Ballard
Автор: Masaki Kashiwara, Pierre Schapira Название: Categories and Sheaves ISBN: 3642066208 ISBN-13(EAN): 9783642066207 Издательство: Springer Рейтинг: Цена: 67070.00 T Наличие на складе: Есть Описание:
Categories and sheaves, which emerged in the middle of the last century as an enrichment for the concepts of sets and functions, appear almost everywhere in mathematics nowadays.
This book covers categories, homological algebra and sheaves in a systematic and exhaustive manner starting from scratch, and continues with full proofs to an exposition of the most recent results in the literature, and sometimes beyond.
The authors present the general theory of categories and functors, emphasising inductive and projective limits, tensor categories, representable functors, ind-objects and localization. Then they study homological algebra including additive, abelian, triangulated categories and also unbounded derived categories using transfinite induction and accessible objects. Finally, sheaf theory as well as twisted sheaves and stacks appear in the framework of Grothendieck topologies.
Автор: Pavel Etingof, Shlomo Gelaki, Dmitri Nikshych, Victor Ostrik Название: Tensor Categories ISBN: 1470434415 ISBN-13(EAN): 9781470434410 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 64680.00 T Наличие на складе: Невозможна поставка. 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: Denis-Charles Cisinski Название: Higher Categories and Homotopical Algebra ISBN: 1108473202 ISBN-13(EAN): 9781108473200 Издательство: Cambridge Academ Рейтинг: Цена: 67590.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This user-friendly book introduces modern homotopy theory through the lens of higher categories after Joyal and Lurie. Starting from scratch it guides graduate students and researchers through the powerful tools that the theory provides for applications in such areas as algebraic geometry, representation theory, algebra and logic.
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: Reiner Hermann Название: Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology ISBN: 1470419955 ISBN-13(EAN): 9781470419950 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 85930.00 T Наличие на складе: Невозможна поставка. Описание: "Volume 243, number 1151 (fourth of 4 numbers), September 2016."
Автор: Tony Pantev, Carlos Simpson, Bertrand Toen, Michel Vaquie, Gabriele Vezzosi Название: Stacks and Categories in Geometry, Topology, and Algebra ISBN: 1470415577 ISBN-13(EAN): 9781470415570 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 104410.00 T Наличие на складе: Невозможна поставка. Описание: This volume contains the proceedings of the CATS4 Conference on Higher Categorical Structures and their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, held from July 2-7, 2012, at CIRM in Luminy, France.Over the past several years, the CATS conference series has brought together top level researchers from around the world interested in relative and higher category theory and its applications to classical mathematical domains.Included in this volume is a collection of articles covering the applications of categories and stacks to geometry, topology and algebra. Techniques such as localization, model categories, simplicial objects, sheaves of categories, mapping stacks, dg structures, hereditary categories, and derived stacks, are applied to give new insight on cluster algebra, Lagrangians, trace theories, loop spaces, structured surfaces, stability, ind-coherent complexes and 1-affineness showing up in geometric Langlands, branching out to many related topics along the way.
Автор: Dennis Gaitsgory, Nick Rozenblyum Название: A Study in Derived Algebraic Geometry: Volume I: Correspondences and Duality ISBN: 1470435691 ISBN-13(EAN): 9781470435691 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 126590.00 T Наличие на складе: Невозможна поставка. Описание: Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in various parts of mathematics, most prominently in representation theory. This volume develops the theory of ind-coherent sheaves in the context of derived algebraic geometry.
Автор: Dennis Gaitsgory, Nick Rozenblyum Название: A Study in Derived Algebraic Geometry: Volume II: Deformations, Lie Theory and Formal Geometry ISBN: 1470435705 ISBN-13(EAN): 9781470435707 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 123810.00 T Наличие на складе: Невозможна поставка. Описание: Derived algebraic geometry is a far-reaching generalization of algebraic geometry. It has found numerous applications in other parts of mathematics, most prominently in representation theory. This volume develops deformation theory, Lie theory and the theory of algebroids in the context of derived algebraic geometry.
Автор: Steffen K?nig; B. Keller; M. Linckelmann; Alexande Название: Derived Equivalences for Group Rings ISBN: 3540643117 ISBN-13(EAN): 9783540643111 Издательство: Springer Рейтинг: Цена: 41880.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Rickard`s Morita theory for derived module categories and its recent applications in representation theory of finite groups. In particular, Broue`s conjecture is discussed, giving a structural explanation for relations between the p-modular character table of a finite group and that of its "p-local structure".
Автор: C.T. Dodson Название: Categories, Bundles and Spacetime Topology ISBN: 9027727716 ISBN-13(EAN): 9789027727718 Издательство: Springer Рейтинг: Цена: 88500.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Gad in Crane Feathers' in R. Brown'The point of a Pin'. van Gulik's TheChinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging SUbdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
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