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Category Theory
Author: Steve Awodey
Publisher: Oxford University Press
ISBN: 0191513822
Pages: 256
Year: 2006-05
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This text and reference book on Category Theory, a branch of abstract algebra, is aimed not only at students of Mathematics, but also researchers and students of Computer Science, Logic, Linguistics, Cognitive Science, Philosophy, and any of the other fields that now make use of it. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of Category Theory understandable to this broad readership. Although it assumes few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads.
Basic Category Theory for Computer Scientists
Author: Benjamin C. Pierce
Publisher: MIT Press
ISBN: 0262660717
Pages: 100
Year: 1991
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Basic Category Theory for Computer Scientists provides a straightforward presentationof the basic constructions and terminology of category theory, including limits, functors, naturaltransformations, adjoints, and cartesian closed categories.
An Introduction to Category Theory
Author: Harold Simmons
Publisher: Cambridge University Press
ISBN: 1139503324
Year: 2011-09-22
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Category theory provides a general conceptual framework that has proved fruitful in subjects as diverse as geometry, topology, theoretical computer science and foundational mathematics. Here is a friendly, easy-to-read textbook that explains the fundamentals at a level suitable for newcomers to the subject. Beginning postgraduate mathematicians will find this book an excellent introduction to all of the basics of category theory. It gives the basic definitions; goes through the various associated gadgetry, such as functors, natural transformations, limits and colimits; and then explains adjunctions. The material is slowly developed using many examples and illustrations to illuminate the concepts explained. Over 200 exercises, with solutions available online, help the reader to access the subject and make the book ideal for self-study. It can also be used as a recommended text for a taught introductory course.
Categories and Computer Science
Author: R. F. C. Walters
Publisher: Cambridge University Press
ISBN: 0521422264
Pages: 166
Year: 1991
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Category Theory has, in recent years, become increasingly important and popular in computer science, and many universities now introduce Category Theory as part of the curriculum for undergraduate computer science students. Here, the theory is developed in a straightforward way, and is enriched with many examples from computer science.
Category Theory in Context
Author: Emily Riehl
Publisher: Courier Dover Publications
ISBN: 0486820807
Pages: 272
Year: 2017-03-09
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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.
Category 7
Author: Bill Evans, Marianna Jameson
Publisher: Forge Books
ISBN: 1429923563
Pages: 384
Year: 2007-07-10
View: 179
Read: 475
A Category 4 hurricane, with winds of up to 155 miles per hour, tears roofs off buildings, smashes windows and doors, and can send floodwaters up to the second floor. Evacuation is suggested for up to six miles inland. Hurricane Katrina was a Category 4 when she made landfall. Hurricane Simone is a Category 7—the biggest, strongest storm in recorded history. When she hits New York City, skyscrapers will fall. Subways and tunnels will flood. Lower Manhattan and much of Queens and Brooklyn will disappear under more than thirty feet of water. All along the Eastern Seaboard, towns and cities are being evacuated as wind-driven rain lashes the coast and storm surges crash through seawalls. Roads are packed with fleeing motorists whose cars are jammed with every personal possession that can be crammed in, plus family members, friends, and beloved pets. A huge natural disaster is brewing in the Atlantic. Except that Simone isn't natural. She's the product of rogue weather science being wielded by billionaire Carter Thompson as part of a personal vendetta against US President Winslow Benson. Once Carter wanted to bring rain to the desert and feed the starving peoples of the planet. Now he wants to show Benson—and the rest of the world—just how powerful wind and water can be. If technology created Simone, perhaps technology can stop her. It's up to Kate Sherman, once a member of Carter's weather team; and Jake Baxter, a weatherman for the CIA, to try, using a secret US Navy weapon. The catch? It has to be deployed inside the hurricane. At the Publisher's request, this title is being sold without Digital Rights Management Software (DRM) applied.
What is Category Theory?
Author: Giandomenico Sica
Publisher: Polimetrica s.a.s.
ISBN: 8876990313
Pages: 290
Year: 2006-01-01
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Author: Edward Gorey
Publisher: Pomegranate
ISBN: 0764937502
Pages: 112
Year: 2006-08-01
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Finally, back in print! Edward Gorey's CATEGORY was first published by Gotham Book Mart in 1974. The English language edition has been out of print for decades. One of Gorey's most beloved books, CATEGORY collects a series of fifty cat vignettes, originally created by the artist as accompaniments to a limited edition of his book Amphigorey. Gorey once said, "I can't conceive of a life without cats." Now Gorey fans and cat lovers alike won't have to conceive of a world without CATEGOREY. Edward Gorey (1925-2000) may be best known for his mildly unsettling illustrated tales and cautionary alphabets—The Deranged Cousins, The Gashlycrumb Tinies, and The Doubtful Guest, among many others. He was also a playwright, an award-winning set and costume designer, and the creator of the animated introductions to the PBS series Mystery!
The Category of the Person
Author: Michael Carrithers, Steven Collins, Steven Lukes
Publisher: Cambridge University Press
ISBN: 0521277574
Pages: 309
Year: 1985-12-27
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The concept that people have of themselves as a 'person' is one of the most intimate notions that they hold. Yet the way in which the category of the person is conceived varies over time and space. In this volume, anthropologists, philosophers, and historians examine the notion of the person in different cultures, past and present. Taking as their starting point a lecture on the person as a category of the human mind, given by Marcel Mauss in 1938, the contributors critically assess Mauss's speculation that notions of the person, rather than being primarily philosophical or psychological, have a complex social and ideological origin. Discussing societies ranging from ancient Greece, India, and China to modern Africa and Papua New Guinea, they provide fascinating descriptions of how these different cultures define the person. But they also raise deeper theoretical issues: What is universally constant and what is culturally variable in people's thinking about the person? How can these variations be explained? Has there been a general progressive development toward the modern Western view of the person? What is distinctive about this? How do one's notions of the person inform one's ability to comprehend alternative formulations? These questions are of compelling interest for a wide range of anthropologists, philosophers, historians, psychologists, sociologists, orientalists, and classicists. The book will appeal to any reader concerned with understanding one of the most fundamental aspects of human existence.
An Introduction to the Language of Category Theory
Author: Steven Roman
Publisher: Birkhäuser
ISBN: 331941917X
Pages: 169
Year: 2017-02-20
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This textbook provides an introduction to elementary category theory, with the aim of making what can be a confusing and sometimes overwhelming subject more accessible. In writing about this challenging subject, the author has brought to bear all of the experience he has gained in authoring over 30 books in university-level mathematics. The goal of this book is to present the five major ideas of category theory: categories, functors, natural transformations, universality, and adjoints in as friendly and relaxed a manner as possible while at the same time not sacrificing rigor. These topics are developed in a straightforward, step-by-step manner and are accompanied by numerous examples and exercises, most of which are drawn from abstract algebra. 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. Chapter 2 is devoted to functors and naturaltransformations, concluding with Yoneda's lemma. Chapter 3 presents the concept of universality and Chapter 4 continues this discussion by exploring cones, limits, and the most common categorical constructions – products, equalizers, pullbacks and exponentials (along with their dual constructions). The chapter concludes with a theorem on the existence of limits. Finally, Chapter 5 covers adjoints and adjunctions. Graduate and advanced undergraduates students in mathematics, computer science, physics, or related fields who need to know or use category theory in their work will find An Introduction to Category Theory to be a concise and accessible resource. It will be particularly useful for those looking for a more elementary treatment of the topic before tackling more advanced texts.
Category Theory
Author: Steve Awodey
Publisher: OUP Oxford
ISBN: 0191612553
Pages: 328
Year: 2010-06-17
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Category theory is a branch of abstract algebra with incredibly diverse applications. This text and reference book is aimed not only at mathematicians, but also researchers and students of computer science, logic, linguistics, cognitive science, philosophy, and any of the other fields in which the ideas are being applied. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of category theory understandable to this broad readership. Although assuming few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided - a must for computer scientists, logicians and linguists! This Second Edition contains numerous revisions to the original text, including expanding the exposition, revising and elaborating the proofs, providing additional diagrams, correcting typographical errors and, finally, adding an entirely new section on monoidal categories. Nearly a hundred new exercises have also been added, many with solutions, to make the book more useful as a course text and for self-study.
Handbook of Categorical Algebra: Volume 1, Basic Category Theory
Author: Francis Borceux
Publisher: Cambridge University Press
ISBN: 0521441781
Pages: 345
Year: 1994-08-26
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The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence, with the first being essentially self-contained, and are accessible to graduate students with a good background in mathematics. In particular, Volume 1, which is devoted to general concepts, can be used for advanced undergraduate courses on category theory.
Aristotle on the Category of Relation
Author: Pamela Michelle Hood
Publisher: University Press of America
ISBN: 0761830073
Pages: 154
Year: 2004
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In Aristotle on the Category of Relation, Pamela Hood challenges the view that Aristotle's conception of relation is so divergent from our own that it does not count as a theory of relation at all. This book presents compelling evidence that Aristotle's theory of relation is more robust than originally suspected.
Category Theory 1991
Author: Robert Andrew George Seely, Canadian Mathematical Society
Publisher: American Mathematical Soc.
ISBN: 0821860186
Pages: 447
Year: 1992-01-01
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As category theory approaches its first half-century, it continues to grow, finding new applications in areas that would have seemed inconceivable a generation ago, as well as in more traditional areas. The language, ideas, and techniques of category theory are well suited to discovering unifying structures in apparently different contexts. Representing this diversity of the field, this book contains the proceedings of an international conference on category theory. The subjects covered here range from topology and geometry to logic and theoretical computer science, from homotopy to braids and conformal field theory. Although generally aimed at experts in the various fields represented, the book will also provide an excellent opportunity for nonexperts to get a feel for the diversity of current applications of category theory.
Categories and Modules with K-Theory in View
Author: A. J. Berrick, M. E. Keating
Publisher: Cambridge University Press
ISBN: 0521632765
Pages: 361
Year: 2000-05-25
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This book, first published in 2000, develops aspects of category theory fundamental to the study of algebraic K-theory. Ring and module theory illustrates category theory which provides insight into more advanced topics in module theory. Starting with categories in general, the text then examines categories of K-theory. This leads to the study of tensor products and the Morita theory. The categorical approach to localizations and completions of modules is formulated in terms of direct and inverse limits, prompting a discussion of localization of categories in general. Finally, local-global techniques which supply information about modules from their localizations and completions and underlie some interesting applications of K-theory to number theory and geometry are considered. Many useful exercises, concrete illustrations of abstract concepts placed in their historical settings and an extensive list of references are included. This book will help all who wish to work in K-theory to master its prerequisites.