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Author : Amnon Neeman
Publisher : Princeton University Press
Page : 468 pages
File Size : 51,7 Mb
Release : 2001-01-23
Category : Mathematics
ISBN : 0691086869

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Triangulated Categories by Amnon Neeman Pdf

The first two chapters of this book offer a modern, self-contained exposition of the elementary theory of triangulated categories and their quotients. The simple, elegant presentation of these known results makes these chapters eminently suitable as a text for graduate students. The remainder of the book is devoted to new research, providing, among other material, some remarkable improvements on Brown's classical representability theorem. In addition, the author introduces a class of triangulated categories"--the "well generated triangulated categories"--and studies their properties. This exercise is particularly worthwhile in that many examples of triangulated categories are well generated, and the book proves several powerful theorems for this broad class. These chapters will interest researchers in the fields of algebra, algebraic geometry, homotopy theory, and mathematical physics.

Author : Brendan Fong,David I. Spivak
Publisher : Cambridge University Press
Page : 351 pages
File Size : 42,7 Mb
Release : 2019-07-18
Category : Computers
ISBN : 9781108482295

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An Invitation to Applied Category Theory by Brendan Fong,David I. Spivak Pdf

Category theory reveals commonalities between structures of all sorts. This book shows its potential in science, engineering, and beyond.

Author : Gabriella Böhm
Publisher : Springer
Page : 165 pages
File Size : 46,5 Mb
Release : 2018-11-01
Category : Mathematics
ISBN : 9783319981376

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Hopf Algebras and Their Generalizations from a Category Theoretical Point of View by Gabriella Böhm Pdf

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.

Author : Ana Agore
Publisher : Springer Nature
Page : 293 pages
File Size : 45,6 Mb
Release : 2024-01-13
Category : Mathematics
ISBN : 9783031428999

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A First Course in Category Theory by Ana Agore Pdf

This textbook provides a first introduction to category theory, a powerful framework and tool for understanding mathematical structures. Designed for students with no previous knowledge of the subject, this book offers a gentle approach to mastering its fundamental principles. Unlike traditional category theory books, which can often be overwhelming for beginners, this book has been carefully crafted to offer a clear and concise introduction to the subject. It covers all the essential topics, including categories, functors, natural transformations, duality, equivalence, (co)limits, and adjunctions. Abundant fully-worked examples guide readers in understanding the core concepts, while complete proofs and instructive exercises reinforce comprehension and promote self-study. The author also provides background material and references, making the book suitable for those with a basic understanding of groups, rings, modules, topological spaces, and set theory. Based on the author's course at the Vrije Universiteit Brussel, the book is perfectly suited for classroom use in a first introductory course in category theory. Its clear and concise style, coupled with its detailed coverage of key concepts, makes it equally suited for self-study.

Author : Anonim
Publisher : Unknown
Page : 222 pages
File Size : 46,7 Mb
Release : 1984
Category : Government publications
ISBN : UOM:39015025196513

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Utah Combined Hydrocarbon Leasing Regional Final EIS: Leasing category amendments by Anonim Pdf

Author : Ricky Tucker
Publisher : Beacon Press
Page : 256 pages
File Size : 52,8 Mb
Release : 2022-01-25
Category : Social Science
ISBN : 9780807003497

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And the Category Is... by Ricky Tucker Pdf

An Electric Literature “Most Anticipated LGBTQ+ Book of 2022” Selection A love letter to the legendary Black and Latinx LGBTQ underground subculture, uncovering its abundant legacy and influence in popular culture. What is Ballroom? Not a song, a documentary, a catchphrase, a TV show, or an individual pop star. It is an underground subculture founded over a century ago by LGBTQ African American and Latino men and women of Harlem. Arts-based and intersectional, it transcends identity, acting as a fearless response to the systemic marginalization of minority populations. Ricky Tucker pulls from his years as a close friend of the community to reveal the complex cultural makeup and ongoing relevance of house and Ballroom, a space where trans lives are respected and applauded, and queer youth are able to find family and acceptance. With each chapter framed as a “category” (Vogue, Realness, Body, et al.), And the Category Is . . . offers an impressionistic point of entry into this subculture, its deeply integrated history, and how it’s been appropriated for mainstream audiences. Each category features an exclusive interview with fierce LGBTQ/POC Ballroom members—Lee Soulja, Benjamin Ninja, Twiggy Pucci Garçon, and more—whose lives, work, and activism drive home that very category. At the height of public intrigue and awareness about Ballroom, thanks to TV shows like FX’s Pose, Tucker’s compelling narratives help us understand its relevance in pop culture, dance, public policy with regard to queer communities, and so much more. Welcome to the norm-defying realness of Ballroom.

Author : Bojko Bakalov,Alexander A. Kirillov
Publisher : American Mathematical Soc.
Page : 232 pages
File Size : 52,8 Mb
Release : 2001
Category : Abelian categories
ISBN : 9780821826867

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Lectures on Tensor Categories and Modular Functors by Bojko Bakalov,Alexander A. Kirillov Pdf

This book gives an exposition of the relations among the following three topics: monoidal tensor categories (such as a category of representations of a quantum group), 3-dimensional topological quantum field theory, and 2-dimensional modular functors (which naturally arise in 2-dimensional conformal field theory). The following examples are discussed in detail: the category of representations of a quantum group at a root of unity and the Wess-Zumino-Witten modular functor. The idea that these topics are related first appeared in the physics literature in the study of quantum field theory. Pioneering works of Witten and Moore-Seiberg triggered an avalanche of papers, both physical and mathematical, exploring various aspects of these relations. Upon preparing to lecture on the topic at MIT, however, the authors discovered that the existing literature was difficult and that there were gaps to fill. The text is wholly expository and finely succinct. It gathers results, fills existing gaps, and simplifies some proofs. The book makes an important addition to the existing literature on the topic. It would be suitable as a course text at the advanced-graduate level.

Author : Emily Riehl
Publisher : Courier Dover Publications
Page : 272 pages
File Size : 45,7 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 : Julia E. Bergner
Publisher : Cambridge University Press
Page : 289 pages
File Size : 46,7 Mb
Release : 2018-03-15
Category : Mathematics
ISBN : 9781107101364

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The Homotopy Theory of (?,1)-Categories by Julia E. Bergner Pdf

An introductory treatment to the homotopy theory of homotopical categories, presenting several models and comparisons between them.

Author : P. G. Romeo,Mikhail V. Volkov,A. R. Rajan
Publisher : Springer Nature
Page : 249 pages
File Size : 43,8 Mb
Release : 2021-03-26
Category : Mathematics
ISBN : 9789813348424

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Semigroups, Categories, and Partial Algebras by P. G. Romeo,Mikhail V. Volkov,A. R. Rajan Pdf

This book is a collection of selected papers presented at the International Conference on Semigroups and Applications, held at the Cochin University of Science and Technology, India, from December 9–12, 2019. This book discusses the recent developments in semigroups theory, category theory and the applications of these in various areas of research, including structure theory of semigroups, lattices, rings and partial algebras. This book presents chapters on ordering orders and quotient rings, block groups and Hall’s relations, quotients of the Booleanization of inverse semigroup, Markov chains through semigroup graph expansions, polycyclic inverse monoids and Thompson group, balanced category and bundle category. This book will be of much value to researchers working in areas of semigroup and operator theory.

Author : Hideto Asashiba
Publisher : American Mathematical Society
Page : 282 pages
File Size : 41,5 Mb
Release : 2022-09-29
Category : Mathematics
ISBN : 9781470464844

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Categories and Representation Theory by Hideto Asashiba Pdf

This book gives a self-contained account of applications of category theory to the theory of representations of algebras. Its main focus is on 2-categorical techniques, including 2-categorical covering theory. The book has few prerequisites beyond linear algebra and elementary ring theory, but familiarity with the basics of representations of quivers and of category theory will be helpful. In addition to providing an introduction to category theory, the book develops useful tools such as quivers, adjoints, string diagrams, and tensor products over a small category; gives an exposition of new advances such as a 2-categorical generalization of Cohen-Montgomery duality in pseudo-actions of a group; and develops the moderation level of categories, first proposed by Levy, to avoid the set theoretic paradox in category theory. The book is accessible to advanced undergraduate and graduate students who would like to study the representation theory of algebras, and it contains many exercises. It can be used as the textbook for an introductory course on the category theoretic approach with an emphasis on 2-categories, and as a reference for researchers in algebra interested in derived equivalences and covering theory.

Author : Kosta Dosen,Zoran Petrić
Publisher : Polimetrica s.a.s.
Page : 155 pages
File Size : 46,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9788876990809

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Proof-net Categories by Kosta Dosen,Zoran Petrić Pdf

Author : Gisa Rauh
Publisher : Oxford University Press
Page : 455 pages
File Size : 49,6 Mb
Release : 2010-06-03
Category : Language Arts & Disciplines
ISBN : 9780199281428

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Syntactic Categories by Gisa Rauh Pdf

This book offers a systematic account of syntactic categories - the building blocks of sentences and the units of grammatical analysis, and explains their description in different formal as well as functional theories of language, including language typology. Its clear and balanced exposition will be widely welcomed by students.

Author : United States. Congress. House. Committee on the Budget
Publisher : Unknown
Page : 20 pages
File Size : 55,8 Mb
Release : 1976
Category : Budget
ISBN : UOM:39015082021521

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Recommendations for Improving the Budget Functional Categories by United States. Congress. House. Committee on the Budget Pdf

Author : Gregory L. Murphy
Publisher : MIT Press
Page : 187 pages
File Size : 40,9 Mb
Release : 2024-01-09
Category : Science
ISBN : 9780262547031

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Categories We Live By by Gregory L. Murphy Pdf

An in-depth analysis of how humanity’s compulsion to categorize affects every aspect of our lived experience. The minute we are born—sometimes even before—we are categorized. From there, classifications dog our every step: to school, work, the doctor’s office, and even the grave. Despite the vast diversity and individuality in every life, we seek patterns, organization, and control. In Categories We Live By, Gregory L. Murphy considers the categories we create to manage life’s sprawling diversity. Analyzing everything from bureaucracy’s innumerable categorizations to the minutiae of language, this book reveals how these categories are imposed on us and how that imposition affects our everyday lives. Categories We Live By explores categorization in two parts. In part one, Murphy introduces the groundwork of categories—how they are created by experts, imperfectly captured by language, and employed by rules. Part two provides a number of case studies. Ranging from trivial categories such as parking regulations and peanut butter to critical issues such as race and mortality, Murphy demonstrates how this need to classify pervades everything. Finally, this comprehensive analysis demonstrates ways that we can cope with categorical disagreements and make categories more useful to our society.