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Author: Benjamin C. Pierce
Publisher: MIT Press
ISBN: 0262326450
Category : Computers
Languages : en
Pages : 117
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Book Description
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
ISBN: 0262326450
Category : Computers
Languages : en
Pages : 117
Get Book Here
Book Description
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
ISBN: 0262320533
Category : Mathematics
Languages : en
Pages : 495
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Book Description
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: Bartosz Milewski
Publisher:
ISBN: 9780464243878
Category :
Languages : en
Pages :
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Book Description
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: R. F. C. Walters
Publisher: Cambridge University Press
ISBN: 9780521422260
Category : Computers
Languages : en
Pages : 180
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Book Description
Category theory has become increasingly important and popular in computer science, and many universities now have introductions to category theory as part of their courses for undergraduate computer scientists. The author is a respected category theorist and has based this textbook on a course given over the last few years at the University of Sydney. The theory is developed in a straightforward way, and is enriched with many examples from computer science. Thus this book meets the needs of undergradute computer scientists, and yet retains a level of mathematical correctness that will broaden its appeal to include students of mathematics new to category theory.
Author: Michael Barr
Publisher:
ISBN:
Category : Computers
Languages : en
Pages : 352
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Book Description
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: Andrea Asperti
Publisher: MIT Press (MA)
ISBN:
Category : Computers
Languages : en
Pages : 330
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Book Description
Category theory is a mathematical subject whose importance in several areas of computer science, most notably the semantics of programming languages and the design of programmes using abstract data types, is widely acknowledged. This book introduces category theory at a level appropriate for computer scientists and provides practical examples in the context of programming language design.
Author: Noson S. Yanofsky
Publisher: Cambridge University Press
ISBN: 9781108792745
Category : Mathematics
Languages : en
Pages : 150
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Book Description
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.
Author: Ralph Krömer
Publisher: Springer Science & Business Media
ISBN: 3764375248
Category : Mathematics
Languages : en
Pages : 400
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Book Description
Category theory is a general mathematical theory of structures and of structures of structures. It occupied a central position in contemporary mathematics as well as computer science. This book describes the history of category theory whereby illuminating its symbiotic relationship to algebraic topology, homological algebra, algebraic geometry and mathematical logic and elaboratively develops the connections with the epistemological significance.
Author: Brendan Fong
Publisher: Cambridge University Press
ISBN: 1108582249
Category : Mathematics
Languages : en
Pages : 351
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Book Description
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: Steve Awodey
Publisher: Oxford University Press
ISBN: 0199587361
Category : Mathematics
Languages : en
Pages : 328
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Book Description
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.
