Basic Category Theory For Computer Scientists
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Author |
: Benjamin C. Pierce |
Publisher |
: MIT Press |
Total Pages |
: 117 |
Release |
: 1991-08-07 |
ISBN-10 |
: 9780262326452 |
ISBN-13 |
: 0262326450 |
Rating |
: 4/5 (52 Downloads) |
Synopsis Basic Category Theory for Computer Scientists by : Benjamin C. Pierce
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. 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. Contents Tutorial • Applications • Further Reading
Author |
: Benjamin C. Pierce |
Publisher |
: MIT Press |
Total Pages |
: 126 |
Release |
: 1991-08-07 |
ISBN-10 |
: 0262660717 |
ISBN-13 |
: 9780262660716 |
Rating |
: 4/5 (17 Downloads) |
Synopsis Basic Category Theory for Computer Scientists by : Benjamin C. Pierce
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. 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. Contents Tutorial • Applications • Further Reading
Author |
: David I. Spivak |
Publisher |
: MIT Press |
Total Pages |
: 495 |
Release |
: 2014-10-17 |
ISBN-10 |
: 9780262320535 |
ISBN-13 |
: 0262320533 |
Rating |
: 4/5 (35 Downloads) |
Synopsis Category Theory for the Sciences by : David I. Spivak
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 |
: Michael Barr |
Publisher |
: |
Total Pages |
: 352 |
Release |
: 1995 |
ISBN-10 |
: UOM:39015034447873 |
ISBN-13 |
: |
Rating |
: 4/5 (73 Downloads) |
Synopsis Category Theory for Computing Science by : Michael Barr
A wide coverage of topics in category theory and computer science is developed in this text, including introductory treatments of cartesian closed categories, sketches and elementary categorical model theory, and triples. Over 300 exercises are included.
Author |
: Tom Leinster |
Publisher |
: Cambridge University Press |
Total Pages |
: 193 |
Release |
: 2014-07-24 |
ISBN-10 |
: 9781107044241 |
ISBN-13 |
: 1107044243 |
Rating |
: 4/5 (41 Downloads) |
Synopsis Basic Category Theory by : Tom Leinster
A short introduction ideal for students learning category theory for the first time.
Author |
: Marco Grandis |
Publisher |
: World Scientific |
Total Pages |
: 390 |
Release |
: 2021-03-05 |
ISBN-10 |
: 9789811236105 |
ISBN-13 |
: 9811236100 |
Rating |
: 4/5 (05 Downloads) |
Synopsis Category Theory And Applications: A Textbook For Beginners (Second Edition) by : Marco Grandis
Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots.This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers the basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications.A reader should have some elementary knowledge of these three subjects, or at least two of them, in order to be able to follow the main examples, appreciate the unifying power of the categorical approach, and discover the subterranean links brought to light and formalised by this perspective.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications in Algebra and Topology, with a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.In this second edition, the book has been entirely reviewed, adding many applications and exercises. All non-obvious exercises have now a solution (or a reference, in the case of an advanced topic); solutions are now collected in the last chapter.
Author |
: Bartosz Milewski |
Publisher |
: |
Total Pages |
: |
Release |
: 2019-08-24 |
ISBN-10 |
: 0464243874 |
ISBN-13 |
: 9780464243878 |
Rating |
: 4/5 (74 Downloads) |
Synopsis Category Theory for Programmers (New Edition, Hardcover) by : Bartosz Milewski
Category Theory is one of the most abstract branches of mathematics. It is usually taught to graduate students after they have mastered several other branches of mathematics, like algebra, topology, and group theory. It might, therefore, come as a shock that the basic concepts of category theory can be explained in relatively simple terms to anybody with some experience in programming.That's because, just like programming, category theory is about structure. Mathematicians discover structure in mathematical theories, programmers discover structure in computer programs. Well-structured programs are easier to understand and maintain and are less likely to contain bugs. Category theory provides the language to talk about structure and learning it will make you a better programmer.
Author |
: Steve Awodey |
Publisher |
: Oxford University Press |
Total Pages |
: 328 |
Release |
: 2010-06-17 |
ISBN-10 |
: 9780199587360 |
ISBN-13 |
: 0199587361 |
Rating |
: 4/5 (60 Downloads) |
Synopsis Category Theory by : Steve Awodey
A comprehensive reference to category theory for students and researchers in mathematics, computer science, logic, cognitive science, linguistics, and philosophy. Useful for self-study and as a course text, the book includes all basic definitions and theorems (with full proofs), as well as numerous examples and exercises.
Author |
: Brendan Fong |
Publisher |
: Cambridge University Press |
Total Pages |
: 351 |
Release |
: 2019-07-18 |
ISBN-10 |
: 9781108482295 |
ISBN-13 |
: 1108482295 |
Rating |
: 4/5 (95 Downloads) |
Synopsis An Invitation to Applied Category Theory by : Brendan Fong
Category theory reveals commonalities between structures of all sorts. This book shows its potential in science, engineering, and beyond.
Author |
: Harold Simmons |
Publisher |
: Cambridge University Press |
Total Pages |
: 237 |
Release |
: 2011-09-22 |
ISBN-10 |
: 9781139503327 |
ISBN-13 |
: 1139503324 |
Rating |
: 4/5 (27 Downloads) |
Synopsis An Introduction to Category Theory by : Harold Simmons
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.