An Invitation To Applied Category Theory

Author : Brendan Fong
Publisher : Cambridge University Press
ISBN 13 : 1108582249
Total Pages : 351 pages
Book Rating : 4.47/5 ( download)

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Download or read book An Invitation to Applied Category Theory written by Brendan Fong and published by Cambridge University Press. This book was released on 2019-07-18 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.

Author : Brendan Fong
Publisher : Cambridge University Press
ISBN 13 : 1108482295
Total Pages : 351 pages
Book Rating : 4.95/5 ( download)

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Download or read book An Invitation to Applied Category Theory written by Brendan Fong and published by Cambridge University Press. This book was released on 2019-07-18 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory reveals commonalities between structures of all sorts. This book shows its potential in science, engineering, and beyond.

Author : David I. Spivak
Publisher : MIT Press
ISBN 13 : 0262320533
Total Pages : 495 pages
Book Rating : 4.35/5 ( download)

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Download or read book Category Theory for the Sciences written by David I. Spivak and published by MIT Press. This book was released on 2014-10-17 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences. 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.

Author : Harold Simmons
Publisher : Cambridge University Press
ISBN 13 : 1139503324
Total Pages : pages
Book Rating : 4.27/5 ( download)

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Download or read book An Introduction to Category Theory written by Harold Simmons and published by Cambridge University Press. This book was released on 2011-09-22 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Tom Leinster
Publisher : Cambridge University Press
ISBN 13 : 1107044243
Total Pages : 193 pages
Book Rating : 4.41/5 ( download)

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Download or read book Basic Category Theory written by Tom Leinster and published by Cambridge University Press. This book was released on 2014-07-24 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: A short introduction ideal for students learning category theory for the first time.

Author : Colin McLarty
Publisher : Clarendon Press
ISBN 13 : 0191589497
Total Pages : 282 pages
Book Rating : 4.92/5 ( download)

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Download or read book Elementary Categories, Elementary Toposes written by Colin McLarty and published by Clarendon Press. This book was released on 1992-06-04 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers elementary aspects of category theory and topos theory. It has few mathematical prerequisites, and uses categorical methods throughout rather than beginning with set theoretic foundations. It works with key notions such as cartesian closedness, adjunctions, regular categories, and the internal logic of a topos. Full statements and elementary proofs are given for the central theorems, including the fundamental theorem of toposes, the sheafification theorem, and the construction of Grothendieck toposes over any topos as base. Three chapters discuss applications of toposes in detail, namely to sets, to basic differential geometry, and to recursive analysis. - ;Introduction; PART I: CATEGORIES: Rudimentary structures in a category; Products, equalizers, and their duals; Groups; Sub-objects, pullbacks, and limits; Relations; Cartesian closed categories; Product operators and others; PART II: THE CATEGORY OF CATEGORIES: Functors and categories; Natural transformations; Adjunctions; Slice categories; Mathematical foundations; PART III: TOPOSES: Basics; The internal language; A soundness proof for topos logic; From the internal language to the topos; The fundamental theorem; External semantics; Natural number objects; Categories in a topos; Topologies; PART IV: SOME TOPOSES: Sets; Synthetic differential geometry; The effective topos; Relations in regular categories; Further reading; Bibliography; Index. -

Author : F. William Lawvere
Publisher : Cambridge University Press
ISBN 13 : 0521894859
Total Pages : 409 pages
Book Rating : 4.52/5 ( download)

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Download or read book Conceptual Mathematics written by F. William Lawvere and published by Cambridge University Press. This book was released on 2009-07-30 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.

Author : Rocco Gangle
Publisher : Edinburgh University Press
ISBN 13 : 1474404200
Total Pages : 264 pages
Book Rating : 4.04/5 ( download)

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Download or read book Diagrammatic Immanence written by Rocco Gangle and published by Edinburgh University Press. This book was released on 2016-08-18 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: A renewal of immanent metaphysics through diagrammatic methods and the tools of category theorySpinoza, Peirce and Deleuze are, in different ways, philosophers of immanence. Rocco Gangle addresses the methodological questions raised by a commitment to immanence in terms of how diagrams may be used both as tools and as objects of philosophical investigation. He integrates insights from Spinozist metaphysics, Peircean semiotics and Deleuzes philosophy of difference in conjunction with the formal operations of category theory. Category theory reveals deep structural connections among logic, topology and a variety of different areas of mathematics, and it provides constructive and rigorous concepts for investigating how diagrams work. Gangle introduces the methods of category theory from a philosophical and diagrammatic perspective, allowing philosophers with little or no mathematical training to come to grips with this important field. This coordination of immanent metaphysics, diagrammatic method and category theoretical mathematics opens a new horizon for contemporary thought.

Author : Emily Riehl
Publisher : Courier Dover Publications
ISBN 13 : 0486820807
Total Pages : 272 pages
Book Rating : 4.04/5 ( download)

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Download or read book Category Theory in Context written by Emily Riehl and published by Courier Dover Publications. This book was released on 2017-03-09 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Noson S. Yanofsky
Publisher : Cambridge University Press
ISBN 13 : 1108890679
Total Pages : 148 pages
Book Rating : 4.70/5 ( download)

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Download or read book Theoretical Computer Science for the Working Category Theorist written by Noson S. Yanofsky and published by Cambridge University Press. This book was released on 2022-03-03 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using basic category theory, this Element describes all the central concepts and proves the main theorems of theoretical computer science. Category theory, which works with functions, processes, and structures, is uniquely qualified to present the fundamental results of theoretical computer science. In this Element, readers will meet some of the deepest ideas and theorems of modern computers and mathematics, such as Turing machines, unsolvable problems, the P=NP question, Kurt Gödel's incompleteness theorem, intractable problems, cryptographic protocols, Alan Turing's Halting problem, and much more. The concepts come alive with many examples and exercises.