Cohomology Of Monoids In Monoidal Categories

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The Cohomology of Monoids

Author : Antonio M. Cegarra
Publisher : Springer Nature
ISBN 13 : 3031502582
Total Pages : 227 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis The Cohomology of Monoids by : Antonio M. Cegarra

Download or read book The Cohomology of Monoids written by Antonio M. Cegarra and published by Springer Nature. This book was released on 2024 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zusammenfassung: This monograph covers topics in the cohomology of monoids up through recent developments. Jonathan Leech's original monograph in the Memoirs of the American Mathematical Society dates back to 1975. This book is an organized, accessible, and self-contained account of this cohomology that includes more recent significant developments that were previously scattered among various publications, along with completely new material. It summarizes the original Leech theory and provides a modern and thorough treatment of the cohomological classification of coextensions of both monoids and monoidal groupoids, including the case of monoids with operators. This cohomology is also compared to the classical Eilenberg-Mac Lane and Hochschild-Mitchell cohomologies. Connections are also established with the Lausch-Loganathan cohomology theory for inverse semigroups, the Gabriel-Zisman cohomology of simplicial sets, the Wells cohomology of small categories (also known as Baues-Wirsching cohomology), Grothendieck sheaf cohomology, and finally Beck's triple cohomology. It also establishes connections with Grillet's cohomology theory for commutative semigroups. The monograph is aimed at researchers in the theory of monoids, or even semigroups, and its interface with category theory, homological algebra, and related fields. However, it is also written to be accessible to graduate students in mathematics and mathematicians in general

Cohomology of Monoids in Monoidal Categories

Author : Hans-Joachim Baues
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.:/5 (247 download)

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Book Synopsis Cohomology of Monoids in Monoidal Categories by : Hans-Joachim Baues

Download or read book Cohomology of Monoids in Monoidal Categories written by Hans-Joachim Baues and published by . This book was released on 1995 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Operads: Proceedings of Renaissance Conferences

Author : Jean-Louis Loday
Publisher : American Mathematical Soc.
ISBN 13 : 0821805134
Total Pages : 458 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Operads: Proceedings of Renaissance Conferences by : Jean-Louis Loday

Download or read book Operads: Proceedings of Renaissance Conferences written by Jean-Louis Loday and published by American Mathematical Soc.. This book was released on 1997 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Monoids, Acts and Categories

Author : Mati Kilp
Publisher : Walter de Gruyter
ISBN 13 : 3110812908
Total Pages : 549 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Monoids, Acts and Categories by : Mati Kilp

Download or read book Monoids, Acts and Categories written by Mati Kilp and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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)

Lectures on Logarithmic Algebraic Geometry

Author : Arthur Ogus
Publisher : Cambridge University Press
ISBN 13 : 1107187737
Total Pages : 559 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Lectures on Logarithmic Algebraic Geometry by : Arthur Ogus

Download or read book Lectures on Logarithmic Algebraic Geometry written by Arthur Ogus and published by Cambridge University Press. This book was released on 2018-11-08 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction to logarithmic geometry, a key tool for analyzing compactification and degeneration in algebraic geometry.

Monoidal Functors, Species and Hopf Algebras

Author : Marcelo Aguiar
Publisher : American Mathematical Soc.
ISBN 13 : 9780821847763
Total Pages : 784 pages
Book Rating : 4.8/5 (477 download)

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Book Synopsis Monoidal Functors, Species and Hopf Algebras by : Marcelo Aguiar

Download or read book Monoidal Functors, Species and Hopf Algebras written by Marcelo Aguiar and published by American Mathematical Soc.. This book was released on 2010 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph integrates ideas from category theory, algebra and combinatorics. It is organized in three parts. Part I belongs to the realm of category theory. It reviews some of the foundational work of Benabou, Eilenberg, Kelly and Mac Lane on monoidal categories and of Joyal and Street on braided monoidal categories, and proceeds to study higher monoidal categories and higher monoidal functors. Special attention is devoted to the notion of a bilax monoidal functor which plays a central role in this work. Combinatorics and geometry are the theme of Part II. Joyal's species constitute a good framework for the study of algebraic structures associated to combinatorial objects. This part discusses the category of species focusing particularly on the Hopf monoids therein. The notion of a Hopf monoid in species parallels that of a Hopf algebra and reflects the manner in which combinatorial structures compose and decompose. Numerous examples of Hopf monoids are given in the text. These are constructed from combinatorial and geometric data and inspired by ideas of Rota and Tits' theory of Coxeter complexes. Part III is of an algebraic nature and shows how ideas in Parts I and II lead to a unified approach to Hopf algebras. The main step is the construction of Fock functors from species to graded vector spaces. These functors are bilax monoidal and thus translate Hopf monoids in species to graded Hopf algebras. This functorial construction of Hopf algebras encompasses both quantum groups and the Hopf algebras of recent prominence in the combinatorics literature. The monograph opens a vast new area of research. It is written with clarity and sufficient detail to make it accessible to advanced graduate students.

Calculus of Fractions and Homotopy Theory

Author : Peter Gabriel
Publisher : Springer Science & Business Media
ISBN 13 : 3642858449
Total Pages : 178 pages
Book Rating : 4.6/5 (428 download)

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Book Synopsis Calculus of Fractions and Homotopy Theory by : Peter Gabriel

Download or read book Calculus of Fractions and Homotopy Theory written by Peter Gabriel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of the present work is to present to the reader a particularly nice category for the study of homotopy, namely the homo topic category (IV). This category is, in fact, - according to Chapter VII and a well-known theorem of J. H. C. WHITEHEAD - equivalent to the category of CW-complexes modulo homotopy, i.e. the category whose objects are spaces of the homotopy type of a CW-complex and whose morphisms are homotopy classes of continuous mappings between such spaces. It is also equivalent (I, 1.3) to a category of fractions of the category of topological spaces modulo homotopy, and to the category of Kan complexes modulo homotopy (IV). In order to define our homotopic category, it appears useful to follow as closely as possible methods which have proved efficacious in homo logical algebra. Our category is thus the" topological" analogue of the derived category of an abelian category (VERDIER). The algebraic machinery upon which this work is essentially based includes the usual grounding in category theory - summarized in the Dictionary - and the theory of categories of fractions which forms the subject of the first chapter of the book. The merely topological machinery reduces to a few properties of Kelley spaces (Chapters I and III). The starting point of our study is the category ,10 Iff of simplicial sets (C.S.S. complexes or semi-simplicial sets in a former terminology).

From Categories to Homotopy Theory

Author : Birgit Richter
Publisher : Cambridge University Press
ISBN 13 : 1108847625
Total Pages : 402 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis From Categories to Homotopy Theory by : Birgit Richter

Download or read book From Categories to Homotopy Theory written by Birgit Richter and published by Cambridge University Press. This book was released on 2020-04-16 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.

Cohomology of Monoidal Categories and Non-abelian Group Cohomology

Author : Lucian M. Ionescu
Publisher :
ISBN 13 :
Total Pages : 218 pages
Book Rating : 4.:/5 (453 download)

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Book Synopsis Cohomology of Monoidal Categories and Non-abelian Group Cohomology by : Lucian M. Ionescu

Download or read book Cohomology of Monoidal Categories and Non-abelian Group Cohomology written by Lucian M. Ionescu and published by . This book was released on 2000 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology

Author : Reiner Hermann:
Publisher : American Mathematical Soc.
ISBN 13 : 1470419955
Total Pages : 158 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology by : Reiner Hermann:

Download or read book Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology written by Reiner Hermann: and published by American Mathematical Soc.. This book was released on 2016-09-06 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, the author extends S. Schwede's exact sequence interpretation of the Gerstenhaber bracket in Hochschild cohomology to certain exact and monoidal categories. Therefore the author establishes an explicit description of an isomorphism by A. Neeman and V. Retakh, which links Ext-groups with fundamental groups of categories of extensions and relies on expressing the fundamental group of a (small) category by means of the associated Quillen groupoid. As a main result, the author shows that his construction behaves well with respect to structure preserving functors between exact monoidal categories. The author uses his main result to conclude, that the graded Lie bracket in Hochschild cohomology is an invariant under Morita equivalence. For quasi-triangular bialgebras, he further determines a significant part of the Lie bracket's kernel, and thereby proves a conjecture by L. Menichi. Along the way, the author introduces n-extension closed and entirely extension closed subcategories of abelian categories, and studies some of their properties.

Tensor Categories

Author : Pavel Etingof
Publisher : American Mathematical Soc.
ISBN 13 : 1470434415
Total Pages : 362 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Tensor Categories by : Pavel Etingof

Download or read book Tensor Categories written by Pavel Etingof and published by American Mathematical Soc.. This book was released on 2016-08-05 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic $K$-Theory

Author : Paul Gregory Goerss
Publisher : American Mathematical Soc.
ISBN 13 : 0821832859
Total Pages : 520 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic $K$-Theory by : Paul Gregory Goerss

Download or read book Homotopy Theory: Relations with Algebraic Geometry, Group Cohomology, and Algebraic $K$-Theory written by Paul Gregory Goerss and published by American Mathematical Soc.. This book was released on 2004 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: As part of its series of Emphasis Years in Mathematics, Northwestern University hosted an International Conference on Algebraic Topology. The purpose of the conference was to develop new connections between homotopy theory and other areas of mathematics. This proceedings volume grew out of that event. Topics discussed include algebraic geometry, cohomology of groups, algebraic $K$-theory, and $\mathbb{A 1$ homotopy theory. Among the contributors to the volume were Alejandro Adem,Ralph L. Cohen, Jean-Louis Loday, and many others. The book is suitable for graduate students and research mathematicians interested in homotopy theory and its relationship to other areas of mathematics.

Lectures on Factorization Homology, ∞-Categories, and Topological Field Theories

Author : Hiro Lee Tanaka
Publisher : Springer Nature
ISBN 13 : 3030611639
Total Pages : 84 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Lectures on Factorization Homology, ∞-Categories, and Topological Field Theories by : Hiro Lee Tanaka

Download or read book Lectures on Factorization Homology, ∞-Categories, and Topological Field Theories written by Hiro Lee Tanaka and published by Springer Nature. This book was released on 2020-12-14 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an informal and geodesic introduction to factorization homology, focusing on providing intuition through simple examples. Along the way, the reader is also introduced to modern ideas in homotopy theory and category theory, particularly as it relates to the use of infinity-categories. As with the original lectures, the text is meant to be a leisurely read suitable for advanced graduate students and interested researchers in topology and adjacent fields.

Model Categories

Author : Mark Hovey
Publisher : American Mathematical Soc.
ISBN 13 : 0821843613
Total Pages : 229 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Model Categories by : Mark Hovey

Download or read book Model Categories written by Mark Hovey and published by American Mathematical Soc.. This book was released on 2007 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model categories are used as a tool for inverting certain maps in a category in a controllable manner. They are useful in diverse areas of mathematics. This book offers a comprehensive study of the relationship between a model category and its homotopy category. It develops the theory of model categories, giving a development of the main examples.

Models, Logics, and Higher-dimensional Categories

Author : Bradd T. Hart
Publisher : American Mathematical Soc.
ISBN 13 : 0821883828
Total Pages : 440 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Models, Logics, and Higher-dimensional Categories by : Bradd T. Hart

Download or read book Models, Logics, and Higher-dimensional Categories written by Bradd T. Hart and published by American Mathematical Soc.. This book was released on with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of a conference held at Centre de recherches mathematiques of the Universite de Montreal, June 18-20, 2009.

Operads And Universal Algebra - Proceedings Of The International Conference

Author : Chengming Bai
Publisher : World Scientific
ISBN 13 : 9814458333
Total Pages : 318 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Operads And Universal Algebra - Proceedings Of The International Conference by : Chengming Bai

Download or read book Operads And Universal Algebra - Proceedings Of The International Conference written by Chengming Bai and published by World Scientific. This book was released on 2012-02-23 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book aims to exemplify the recent developments in operad theory, in universal algebra and related topics in algebraic topology and theoretical physics. The conference has established a better connection between mathematicians working on operads (mainly the French team) and mathematicians working in universal algebra (primarily the Chinese team), and to exchange problems, methods and techniques from these two subject areas.

Monoids And Semigroups With Applications - Proceedings Of The Berkeley Workshop In Monoids

Author : John Rhodes
Publisher : #N/A
ISBN 13 : 9814612715
Total Pages : 548 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Monoids And Semigroups With Applications - Proceedings Of The Berkeley Workshop In Monoids by : John Rhodes

Download or read book Monoids And Semigroups With Applications - Proceedings Of The Berkeley Workshop In Monoids written by John Rhodes and published by #N/A. This book was released on 1991-03-06 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the Berkeley Workshop on Monoids was to give expository talks by the most qualified experts in the emerging main areas of monoid and semigroup theory including applications to theoretical computer science. This was supplemented with current research papers. The topics covered, in an accessible way for the mathematical and theoretical computer community, were: Kernels and expansions in semigroup theory; Implicit operations; Inverse monoids; Varieties of semigroups and universal algebra; Linear semigroups and monoids of Lie type; Monoids acting on tress; Synthesis theorem, regular semigroups, and applications; Type-II conjecture; Application to theoretical computer science and decision problems.