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    Category Theory


    1. 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)1788USD$17.88
    US$52.25
    US$2.75 (5%)
    Category: Hardcover (2014-10-10)
    Publisher: The MIT Press
    ISBN: 0262028131
    Sales Rank: 395814
    Lowest New Price: $39.44
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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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    1. Elementary Applied Topology
    2. Conceptual Mathematics: A First Introduction to Categories
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    5. Categories for the Working Mathematician (Graduate Texts in Mathematics)
    6. Purely Functional Data Structures
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    10. An Introduction to Category Theory .


    2. 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)1322USD$13.22
    US$52.70
    US$9.3 (15%)
    Category: Paperback Brand: imusti
    (2010-08-13)
    Publisher: Oxford University Press
    ISBN: 0199237182
    Sales Rank: 634175
    Lowest New Price: $40.19
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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)
    3. Conceptual Mathematics: A First Introduction to Categories
    4. Topoi: The Categorial Analysis of Logic (Dover Books on Mathematics)
    5. Category Theory in Context (Aurora: Dover Modern Math Originals)
    6. Types and Programming Languages (MIT Press)
    7. An Introduction to Category Theory
    8. Basic Category Theory for Computer Scientists (Foundations of Computing)
    9. Basic Category Theory (Cambridge Studies in Advanced Mathematics)
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    3. Category Theory in Context (Aurora: Dover Modern Math Originals)
    by Emily Riehl
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    US$29.95
    US$24.38
    US$5.57 (19%)
    Category: Paperback Brand: imusti
    (2016-11-16)
    Publisher: Dover Publications
    ISBN: 048680903X
    Sales Rank: 136672
    Lowest New Price: $16.42
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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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    4. 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)683USD$6.83
    US$33.41
    US$1.59 (5%)
    Category: Paperback Brand: imusti
    (1991-08-07)
    Publisher: The MIT Press
    ISBN: 0262660717
    Sales Rank: 794175
    Lowest New Price: $24.24
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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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    2. Purely Functional Data Structures
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    4. Category Theory for the Sciences (MIT Press)
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    6. The Little Prover (MIT Press)
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    8. A Book of Abstract Algebra: Second Edition (Dover Books on Mathematics)
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    10. Advanced Topics in Types and Programming Languages (MIT Press) .


    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)1501USD$15.01
    US$59.96
    US$14.99 (20%)
    Category: Hardcover Brand: imusti
    (1998-09-25)
    Publisher: Springer
    ISBN: 0387984038
    Sales Rank: 248728
    Lowest New Price: $50.99
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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

    Similar Items:
    1. Category Theory (Oxford Logic Guides)
    2. Sheaves in Geometry and Logic: A First Introduction to Topos Theory (Universitext)
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    10. Category Theory in Context (Aurora: Dover Modern Math Originals) .


    6. Category Theory: Questions and Answers
    by George A Duckett
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    US$15.00
    US$15.00
    Category: Paperback Brand: imusti
    (2016-05-25)
    Publisher: CreateSpace Independent Publishing Platform
    ISBN: 1533438889
    Sales Rank: 9920532
    Lowest New Price: $12.25
    Lowest Used Price: $14.36 (3 Used Items)
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    If you have a question about Category Theory this is the book with the answers. Category Theory: Questions and Answers takes some of the best questions and answers asked on the mathoverflow.stackexchange.com website. You can use this book to look up commonly asked questions, browse questions on a particular topic, compare answers to common topics, check out the original source and much more. This book has been designed to be very easy to use, with many internal references set up that makes browsing in many different ways possible. Topics covered include: Algebraic Topology, Algebraic Geometry, Higher Category Theory, Homotopy Theory, Topos Theory, Reference Request, Logic, Group Theory, Monoidal Categories, Homological Algebra, Set Theory, General Topology, Model Categories, Representation Theory, Soft Question, Commutative Algebra, Rings And Algebras, Simplicial Stuff, Sheaf Theory, Limits And Colimits and many more.

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    7. An Introduction to the Language of Category Theory (Compact Textbooks in Mathematics)
    by Steven Roman
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    US$49.99
    US$41.03
    US$8.96 (18%)
    Category: Paperback Brand: imusti
    (2017-01-13)
    Publisher: Birkhäuser
    ISBN: 3319419161
    Sales Rank: 143062
    Lowest New Price: $30.01
    Lowest Used Price: $36.83 (6 Used Items)
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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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    8. Basic Category Theory (Cambridge Studies in Advanced Mathematics)
    by Tom Leinster
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    US$67.00
    US$64.99
    US$2.01 (3%)
    Category: Hardcover Brand: imusti
    (2014-09-22)
    Publisher: Cambridge University Press
    ISBN: 1107044243
    Sales Rank: 1219875
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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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    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: Basic Books AZ
    (2016-05-10)
    Publisher: Basic Books
    ISBN: 0465097677
    Sales Rank: 52326
    Lowest New Price: $10.35
    Lowest Used Price: $5.15 (20 Used Items)
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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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    • Basic Books AZ

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    10. Category Theory
    by J. Klein
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    US$12.95
    US$12.95
    Category: Paperback Brand: Basic Books AZ
    (2015-11-20)
    Publisher: CreateSpace Independent Publishing Platform
    ISBN: 151942857X
    Sales Rank: 2114265
    Lowest New Price: $12.95
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    This book of faux mathematics is professionally bound, looks impressive on your desk, tabletop or bookshelf, and would make a great gift! Whether you are out to prank your students, impress a date, or to make friends, coworkers or your boss think you are way smart, this book is sure to blow their minds. Convincingly super-advanced, they won't understand a word of it, but neither will you, and that's the fun of it! The equations are beautifully typeset using LaTeX, and the chapters are as incomprehensible as they are hilarious. Prank your students, make your boss think you're worth a bigger paycheck, intimidate your coworkers, and impress that hot date - purchase this book now and be a genius! For an extra laugh, donate the book to a library. :-))

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