Category theory for the sciences, Spivak, David I. (research Scientist, Massachusetts Institute Of Technology)
Автор: Leinster Название: Basic Category Theory ISBN: 1107044243 ISBN-13(EAN): 9781107044241 Издательство: Cambridge Academ Рейтинг: Цена: 8237.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Assuming little mathematical background, this short introduction to category theory is ideal for beginning graduate students or advanced undergraduates learning category theory for the first time. Suitable for independent study or as a course book, it gives extensive explanations of the key concepts along with hundreds of examples and exercises.
Автор: S. MacLane; M. Andre; D. A. Buchsbaum; E. Dubuc; R Название: Reports of the Midwest Category Seminar II ISBN: 3540042318 ISBN-13(EAN): 9783540042310 Издательство: Springer Рейтинг: Цена: 3487.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots.This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers the basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications.A reader should have some elementary knowledge of these three subjects, or at least two of them, in order to be able to follow the main examples, appreciate the unifying power of the categorical approach, and discover the subterranean links brought to light and formalised by this perspective.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications in Algebra and Topology, with a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.In this second edition, the book has been entirely reviewed, adding many applications and exercises. All non-obvious exercises have now a solution (or a reference, in the case of an advanced topic); solutions are now collected in the last chapter.
Описание: These lecture notes provide a self-contained introduction to a wide range of generalizations of Hopf algebras. Multiplication of their modules is described by replacing the category of vector spaces with more general monoidal categories, thereby extending the range of applications.Since Sweedler's work in the 1960s, Hopf algebras have earned a noble place in the garden of mathematical structures. Their use is well accepted in fundamental areas such as algebraic geometry, representation theory, algebraic topology, and combinatorics. Now, similar to having moved from groups to groupoids, it is becoming clear that generalizations of Hopf algebras must also be considered. This book offers a unified description of Hopf algebras and their generalizations from a category theoretical point of view. The author applies the theory of liftings to Eilenberg–Moore categories to translate the axioms of each considered variant of a bialgebra (or Hopf algebra) to a bimonad (or Hopf monad) structure on a suitable functor. Covered structures include bialgebroids over arbitrary algebras, in particular weak bialgebras, and bimonoids in duoidal categories, such as bialgebras over commutative rings, semi-Hopf group algebras, small categories, and categories enriched in coalgebras.Graduate students and researchers in algebra and category theory will find this book particularly useful. Including a wide range of illustrative examples, numerous exercises, and completely worked solutions, it is suitable for self-study.
Описание: Exemplifies the developments in operad theory, in universal algebra and related topics in algebraic topology and theoretical physics.
Автор: Lubkin Saul Название: A Non-Hausdorff Completion ISBN: 9814667382 ISBN-13(EAN): 9789814667388 Издательство: World Scientific Publishing Рейтинг: Цена: 11563.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This book introduces entirely new invariants never considered before, in homological algebra and commutative (and even non-commutative) algebra. The C-completion C(M), and higher C-completions, Cn(M), are defined for an arbitrary left module M over a topological ring A. Spectral sequences are defined that use these invariants. Given a left module over a topological ring A, under mild conditions the usual Hausdorff completion: M DEGREES can be recovered from the C-completion C(M), by taking the quotient module by the closure of {0}.
The new invariants and tools in this book are expected to be used in the study of p-adic cohomology in algebraic geometry; and also in the study of p-adic Banach spaces -- by replacing the cumbersome "complete tensor product" of p-adic Banach spaces, with the more sophisticated "C-complete tensor product," discussed in this book.
It is also not unlikely that the further study of these new invariants may well develop into a new branch of abstract mathematics - connected with commutative algebra, homological algebra, and algebraic topology.
Описание: These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled 'Groups, Representations, and Cohomology' and held from June 22 to June 27, 2015 at Sabhal M?r Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of 'Geometric Methods in the Representation Theory of Finite Groups' and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016.
The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.
Автор: S.E. Rodabaugh; Erich Peter Klement; Ulrich H?hle Название: Applications of Category Theory to Fuzzy Subsets ISBN: 9401051569 ISBN-13(EAN): 9789401051569 Издательство: Springer Рейтинг: Цена: 27950.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book has a fundamental relationship to the International Seminar on Fuzzy Set Theory held each September in Linz, Austria. Beginning with the tenth Seminar, the intimate setting was retained, but each Seminar narrowed in theme;
Автор: Steven Roman Название: An Introduction to the Language of Category Theory ISBN: 3319419161 ISBN-13(EAN): 9783319419169 Издательство: Springer Рейтинг: Цена: 7685.00 р. Наличие на складе: Поставка под заказ.
Описание: The first chapter of the book introduces the definitions of category and functor and discusses diagrams,duality, initial and terminal objects, special types of morphisms, and some special types of categories,particularly comma categories and hom-set categories.
Автор: Grandis, Marco (univ Di Genova, Italy) Название: Category theory and applications: a textbook for beginners ISBN: 9813231068 ISBN-13(EAN): 9789813231061 Издательство: World Scientific Publishing Рейтинг: Цена: 14256.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a deeper understanding of their roots.
This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers its basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications.
Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications and a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.
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