Monoids Acts And Categories

Author : Mati Kilp,Ulrich Knauer,Alexander V. Mikhalev
Publisher : Walter de Gruyter
Page : 549 pages
File Size : 51,5 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110812909

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Monoids, Acts and Categories by Mati Kilp,Ulrich Knauer,Alexander V. Mikhalev Pdf

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
Page : 433 pages
File Size : 48,8 Mb
Release : 2011-05-02
Category : Mathematics
ISBN : 9783110805697

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Algebra by Yuri Bahturin Pdf

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 : Emily Riehl
Publisher : Courier Dover Publications
Page : 272 pages
File Size : 49,9 Mb
Release : 2017-03-09
Category : Mathematics
ISBN : 9780486820804

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Category Theory in Context by Emily Riehl Pdf

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 : Benjamin Steinberg
Publisher : Springer
Page : 320 pages
File Size : 46,6 Mb
Release : 2016-12-09
Category : Mathematics
ISBN : 9783319439327

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Representation Theory of Finite Monoids by Benjamin Steinberg Pdf

This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles for graduate accessibility, bringing a broad range of advanced readers to the forefront of research in the area. Highlights of the text include applications to probability theory, symbolic dynamics, and automata theory. Comfort with module theory, a familiarity with ordinary group representation theory, and the basics of Wedderburn theory, are prerequisites for advanced graduate level study. Researchers in algebra, algebraic combinatorics, automata theory, and probability theory, will find this text enriching with its thorough presentation of applications of the theory to these fields. Prior knowledge of semigroup theory is not expected for the diverse readership that may benefit from this exposition. The approach taken in this book is highly module-theoretic and follows the modern flavor of the theory of finite dimensional algebras. The content is divided into 7 parts. Part I consists of 3 preliminary chapters with no prior knowledge beyond group theory assumed. Part II forms the core of the material giving a modern module-theoretic treatment of the Clifford –Munn–Ponizovskii theory of irreducible representations. Part III concerns character theory and the character table of a monoid. Part IV is devoted to the representation theory of inverse monoids and categories and Part V presents the theory of the Rhodes radical with applications to triangularizability. Part VI features 3 chapters devoted to applications to diverse areas of mathematics and forms a high point of the text. The last part, Part VII, is concerned with advanced topics. There are also 3 appendices reviewing finite dimensional algebras, group representation theory, and Möbius inversion.

Author : Michael Barr,Charles Wells
Publisher : Unknown
Page : 352 pages
File Size : 43,8 Mb
Release : 1995
Category : Computers
ISBN : UOM:39015034447873

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Category Theory for Computing Science by Michael Barr,Charles Wells Pdf

A wide coverage of topics in category theory and computer science is developed in this text, including introductory treatments of cartesian closed categories, sketches and elementary categorical model theory, and triples. Over 300 exercises are included.

Author : Anonim
Publisher : Unknown
Page : 860 pages
File Size : 41,9 Mb
Release : 2006
Category : Mathematics
ISBN : UOM:39015067268279

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Mathematical Reviews by Anonim Pdf

Author : Saunders Mac Lane
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 51,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475747218

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Categories for the Working Mathematician by Saunders Mac Lane Pdf

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,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik
Publisher : American Mathematical Soc.
Page : 344 pages
File Size : 54,8 Mb
Release : 2016-08-05
Category : Algebraic topology
ISBN : 9781470434410

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Tensor Categories by Pavel Etingof,Shlomo Gelaki,Dmitri Nikshych,Victor Ostrik Pdf

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 : Tom Leinster
Publisher : Cambridge University Press
Page : 193 pages
File Size : 50,9 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9781107044241

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Basic Category Theory by Tom Leinster Pdf

A short introduction ideal for students learning category theory for the first time.

Author : Arthur Ogus
Publisher : Cambridge University Press
Page : 559 pages
File Size : 55,5 Mb
Release : 2018-11-08
Category : Mathematics
ISBN : 9781107187733

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Lectures on Logarithmic Algebraic Geometry by Arthur Ogus Pdf

A self-contained introduction to logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry.

Author : Gregory Maxwell Kelly
Publisher : CUP Archive
Page : 260 pages
File Size : 50,5 Mb
Release : 1982-02-18
Category : Mathematics
ISBN : 0521287022

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Basic Concepts of Enriched Category Theory by Gregory Maxwell Kelly Pdf

Author : J. C. Rosales,P. A. García-Sánchez
Publisher : Nova Publishers
Page : 204 pages
File Size : 45,5 Mb
Release : 1999
Category : Mathematics
ISBN : 1560726709

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Finitely Generated Commutative Monoids by J. C. Rosales,P. A. García-Sánchez Pdf

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 : Bartosz Milewski
Publisher : Unknown
Page : 128 pages
File Size : 40,9 Mb
Release : 2019-08-24
Category : Electronic
ISBN : 0464243874

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Category Theory for Programmers (New Edition, Hardcover) by Bartosz Milewski Pdf

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.

Author : Birgit Richter
Publisher : Cambridge University Press
Page : 401 pages
File Size : 48,6 Mb
Release : 2020-04-16
Category : Mathematics
ISBN : 9781108479622

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From Categories to Homotopy Theory by Birgit Richter Pdf

Bridge the gap between category theory and its applications in homotopy theory with this guide for graduate students and researchers.

Author : Dirk Hofmann,Gavin J. Seal,Walter Tholen
Publisher : Cambridge University Press
Page : 523 pages
File Size : 46,5 Mb
Release : 2014-07-31
Category : Mathematics
ISBN : 9781107063945

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Monoidal Topology by Dirk Hofmann,Gavin J. Seal,Walter Tholen Pdf

Based on lax-algebraic and categorical methods, Monoidal Topology provides a unified theory for metric and topological structures with far-reaching applications.