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    Category Theory in Context
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    Category Theory for
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    Category Theory
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    An Introduction to the
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    Basic Category Theory
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    A Book of Abstract Algebra


    1. Category Theory in Context (Aurora: Dover Modern Math Originals)
    by Emily Riehl
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    Category: Paperback (2016-11-16)
    Publisher: Dover Publications
    ISBN: 048680903X
    Sales Rank: 80278
    Lowest New Price: $16.13
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    Category theory has provided the foundations for many of the twentieth century's greatest advances in pure mathematics. This concise, original text for a one-semester introduction to the subject is derived from courses that author Emily Riehl taught at Harvard and Johns Hopkins Universities. The treatment introduces the essential concepts of category theory: categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads, Kan extensions, and other topics.

    Suitable for advanced undergraduates and graduate students in mathematics, the text provides tools for understanding and attacking difficult problems in algebra, number theory, algebraic geometry, and algebraic topology. Drawing upon a broad range of mathematical examples from the categorical perspective, the author illustrates how the concepts and constructions of category theory arise from and illuminate more basic mathematical ideas. While the reader will be rewarded for familiarity with these background mathematical contexts, essential prerequisites are limited to basic set theory and logic.

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    2. Category Theory for the Sciences (MIT Press)
    by David I. Spivak
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    US$55.00The MIT Press14961409102157301BookABIS_BOOK2014-10-10The MIT PressThe MIT PressCategory Theory for the Sciences (MIT Press)878USD$8.78
    US$52.25
    US$2.75 (5%)
    Category: Hardcover (2014-10-10)
    Publisher: The MIT Press
    ISBN: 0262028131
    Sales Rank: 244163
    Lowest New Price: $35.02
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    Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs -- categories in disguise. After explaining the "big three" concepts of category theory -- categories, functors, and natural transformations -- the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions. Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.

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    6. Categories for the Working Mathematician (Graduate Texts in Mathematics)
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    8. Category Theory in Context (Aurora: Dover Modern Math Originals)
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    10. An Introduction to Category Theory .


    3. Category Theory (Oxford Logic Guides)
    by Steve Awodey
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    US$62.00Oxford University Press133674925127600BookABIS_BOOK2010-08-13Oxford University PressOxford University PressCategory Theory (Oxford Logic Guides)826USD$8.26
    US$58.90
    US$3.1 (5%)
    Category: Paperback Brand: imusti
    (2010-08-13)
    Publisher: Oxford University Press
    ISBN: 0199237182
    Sales Rank: 668009
    Lowest New Price: $40.14
    Lowest Used Price: $38.95 (15 Used Items)
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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.

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    • Oxford University Press USA

    Similar Items:
    1. Categories for the Working Mathematician (Graduate Texts in Mathematics)
    2. Category Theory for the Sciences (MIT Press)
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    5. Category Theory in Context (Aurora: Dover Modern Math Originals)
    6. An Introduction to Category Theory
    7. Types and Programming Languages (MIT Press)
    8. Basic Category Theory for Computer Scientists (Foundations of Computing)
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    10. Basic Category Theory (Cambridge Studies in Advanced Mathematics) .


    4. An Introduction to the Language of Category Theory (Compact Textbooks in Mathematics)
    by Steven Roman
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    US$49.99
    US$49.99
    Category: Paperback Brand: imusti
    (2017-01-13)
    Publisher: Birkhäuser
    ISBN: 3319419161
    Sales Rank: 967810
    Lowest New Price: $33.27
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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 natural
    transformations, 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.

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    2. Basic Category Theory (Cambridge Studies in Advanced Mathematics)
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    6. Introduction To Commutative Algebra, Student Economy Edition
    7. Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics)
    8. Turing's Vision: The Birth of Computer Science (MIT Press)
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    10. TENSORS made easy with SOLVED PROBLEMS .


    5. Categories for the Working Mathematician (Graduate Texts in Mathematics)
    by Saunders Mac Lane
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    US$74.95Springer13171029211376141BookABIS_BOOK1998-09-25SpringerSpringerCategories for the Working Mathematician (Graduate Texts in Mathematics)1138USD$11.38
    US$63.37
    US$11.58 (15%)
    Category: Hardcover Brand: imusti
    (1998-09-25)
    Publisher: Springer
    ISBN: 0387984038
    Sales Rank: 449991
    Lowest New Price: $51.04
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    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.

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    • Springer

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    6. An Introduction to Category Theory
    by Harold Simmons
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    US$35.99Cambridge University Press123854898925981BookABIS_BOOK2011-11-21Cambridge University Press2011-09-22Cambridge University PressAn Introduction to Category Theory548USD$5.48
    US$35.99
    US$0 (0%)
    Category: Paperback Brand: Brand: Cambridge University Press
    (2011-11-21)
    Publisher: Cambridge University Press
    ISBN: 0521283043
    Sales Rank: 713336
    Lowest New Price: $23.65
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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.

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    • Used Book in Good Condition

    Similar Items:
    1. Category Theory for the Sciences (MIT Press)
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    5. Conceptual Mathematics: A First Introduction to Categories
    6. Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics)
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    10. Categories for the Working Mathematician (Graduate Texts in Mathematics) .


    7. Basic Category Theory (Cambridge Studies in Advanced Mathematics)
    by Tom Leinster
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    US$67.00Cambridge University Press119063874885911BookABIS_BOOK2014-09-22Cambridge University PressCambridge University PressBasic Category Theory (Cambridge Studies in Advanced Mathematics)735USD$7.35
    US$64.99
    US$2.01 (3%)
    Category: Hardcover Brand: Brand: Cambridge University Press
    (2014-09-22)
    Publisher: Cambridge University Press
    ISBN: 1107044243
    Sales Rank: 815442
    Lowest New Price: $58.47
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    At the heart of this short introduction to category theory is the idea of a universal property, important throughout mathematics. After an introductory chapter giving the basic definitions, separate chapters explain three ways of expressing universal properties: via adjoint functors, representable functors, and limits. A final chapter ties all three together. The book is suitable for use in courses or for independent study. Assuming relatively little mathematical background, it is ideal for beginning graduate students or advanced undergraduates learning category theory for the first time. For each new categorical concept, a generous supply of examples is provided, taken from different parts of mathematics. At points where the leap in abstraction is particularly great (such as the Yoneda lemma), the reader will find careful and extensive explanations. Copious exercises are included.

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    8. Basic Category Theory for Computer Scientists (Foundations of Computing)
    by Benjamin C. Pierce
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    US$35.00The MIT Press111450910557001BookABIS_BOOK1991-08-07The MIT PressThe MIT PressBasic Category Theory for Computer Scientists (Foundations of Computing)954USD$9.54
    US$35.00
    US$0 (0%)
    Category: Paperback Brand: imusti
    (1991-08-07)
    Publisher: The MIT Press
    ISBN: 0262660717
    Sales Rank: 215970
    Lowest New Price: $22.54
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    Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Benjamin C. Pierce received his doctoral degree from Carnegie Mellon University.Contents : Tutorial. Applications. Further Reading.

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    • Mit Press

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    9. How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics
    by Eugenia Cheng
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    US$15.99
    US$10.35
    US$5.64 (35%)
    Category: Paperback Brand: imusti
    (2016-05-10)
    Publisher: Basic Books
    ISBN: 0465097677
    Sales Rank: 9864
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    What is math? How exactly does it work? And what do three siblings trying to share a cake have to do with it? In How to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen. We learn how the béchamel in a lasagna can be a lot like the number five, and why making a good custard proves that math is easy but life is hard. At the heart of it all is Cheng's work on category theory, a cutting-edge “mathematics of mathematics,” that is about figuring out how math works.

    Combined with her infectious enthusiasm for cooking and true zest for life, Cheng's perspective on math is a funny journey through a vast territory no popular book on math has explored before. So, what is math? Let's look for the answer in the kitchen.

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    10. A Book of Abstract Algebra: Second Edition (Dover Books on Mathematics)
    by Charles C Pinter
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    US$18.95
    US$13.24
    US$5.71 (30%)
    Category: Paperback Brand: imusti
    (2010-01-14)
    Publisher: Dover Publications
    ISBN: 0486474178
    Sales Rank: 19429
    Lowest New Price: $10.00
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    Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. Intended for undergraduate courses in abstract algebra, it is suitable for junior- and senior-level math majors and future math teachers. This second edition features additional exercises to improve student familiarity with applications.
    An introductory chapter traces concepts of abstract algebra from their historical roots. Succeeding chapters avoid the conventional format of definition-theorem-proof-corollary-example; instead, they take the form of a discussion with students, focusing on explanations and offering motivation. Each chapter rests upon a central theme, usually a specific application or use. The author provides elementary background as needed and discusses standard topics in their usual order. He introduces many advanced and peripheral subjects in the plentiful exercises, which are accompanied by ample instruction and commentary and offer a wide range of experiences to students at different levels of ability.

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    • Dover Publications

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