Monoids Acts And Categories
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Author |
: Mati Kilp |
Publisher |
: Walter de Gruyter |
Total Pages |
: 549 |
Release |
: 2011-06-24 |
ISBN-10 |
: 9783110812909 |
ISBN-13 |
: 3110812908 |
Rating |
: 4/5 (09 Downloads) |
Synopsis Monoids, Acts and Categories by : Mati Kilp
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
Author |
: Yuri Bahturin |
Publisher |
: Walter de Gruyter |
Total Pages |
: 433 |
Release |
: 2011-05-02 |
ISBN-10 |
: 9783110805697 |
ISBN-13 |
: 3110805693 |
Rating |
: 4/5 (97 Downloads) |
Synopsis Algebra by : Yuri Bahturin
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Author |
: Saunders Mac Lane |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 320 |
Release |
: 2013-04-17 |
ISBN-10 |
: 9781475747218 |
ISBN-13 |
: 1475747217 |
Rating |
: 4/5 (18 Downloads) |
Synopsis Categories for the Working Mathematician by : Saunders Mac Lane
An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. 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.
Author |
: Pavel Etingof |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 362 |
Release |
: 2016-08-05 |
ISBN-10 |
: 9781470434410 |
ISBN-13 |
: 1470434415 |
Rating |
: 4/5 (10 Downloads) |
Synopsis Tensor Categories by : Pavel Etingof
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.
Author |
: J. C. Rosales |
Publisher |
: Nova Publishers |
Total Pages |
: 204 |
Release |
: 1999 |
ISBN-10 |
: 1560726709 |
ISBN-13 |
: 9781560726708 |
Rating |
: 4/5 (09 Downloads) |
Synopsis Finitely Generated Commutative Monoids by : J. C. Rosales
A textbook for an undergraduate course, requiring only a knowledge of basic linear algebra. Explains how to compute presentations for finitely generated cancellative monoids, and from a presentation of a monoid, decide whether this monoid is cancellative, reduced, separative, finite, torsion free, group, affine, full, normal, etc. Of most interest to people working with semigroup theory, but also in other areas of algebra. Annotation copyrighted by Book News, Inc., Portland, OR
Author |
: Emily Riehl |
Publisher |
: Courier Dover Publications |
Total Pages |
: 273 |
Release |
: 2017-03-09 |
ISBN-10 |
: 9780486820804 |
ISBN-13 |
: 0486820807 |
Rating |
: 4/5 (04 Downloads) |
Synopsis Category Theory in Context by : Emily Riehl
Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.
Author |
: |
Publisher |
: |
Total Pages |
: 860 |
Release |
: 2006 |
ISBN-10 |
: UOM:39015067268279 |
ISBN-13 |
: |
Rating |
: 4/5 (79 Downloads) |
Synopsis Mathematical Reviews by :
Author |
: Arthur Ogus |
Publisher |
: Cambridge University Press |
Total Pages |
: 559 |
Release |
: 2018-11-08 |
ISBN-10 |
: 9781107187733 |
ISBN-13 |
: 1107187737 |
Rating |
: 4/5 (33 Downloads) |
Synopsis Lectures on Logarithmic Algebraic Geometry by : Arthur Ogus
A self-contained introduction to logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry.
Author |
: Tom Leinster |
Publisher |
: Cambridge University Press |
Total Pages |
: 193 |
Release |
: 2014-07-24 |
ISBN-10 |
: 9781107044241 |
ISBN-13 |
: 1107044243 |
Rating |
: 4/5 (41 Downloads) |
Synopsis Basic Category Theory by : Tom Leinster
A short introduction ideal for students learning category theory for the first time.
Author |
: Bartosz Milewski |
Publisher |
: |
Total Pages |
: |
Release |
: 2019-08-24 |
ISBN-10 |
: 0464243874 |
ISBN-13 |
: 9780464243878 |
Rating |
: 4/5 (74 Downloads) |
Synopsis Category Theory for Programmers (New Edition, Hardcover) by : Bartosz Milewski
Category Theory is one of the most abstract branches of mathematics. It is usually taught to graduate students after they have mastered several other branches of mathematics, like algebra, topology, and group theory. It might, therefore, come as a shock that the basic concepts of category theory can be explained in relatively simple terms to anybody with some experience in programming.That's because, just like programming, category theory is about structure. Mathematicians discover structure in mathematical theories, programmers discover structure in computer programs. Well-structured programs are easier to understand and maintain and are less likely to contain bugs. Category theory provides the language to talk about structure and learning it will make you a better programmer.