Theoretical Computer Science for the Working Category Theorist

2022-03-03
Theoretical Computer Science for the Working Category Theorist
Author: Noson S. Yanofsky
Publisher: Cambridge University Press
Total Pages: 150
Release: 2022-03-03
Genre: Mathematics
ISBN: 9781108792745
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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.

An Invitation to Applied Category Theory

2019-07-18
An Invitation to Applied Category Theory
Author: Brendan Fong
Publisher: Cambridge University Press
Total Pages: 351
Release: 2019-07-18
Genre: Mathematics
ISBN: 1108582249
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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.

Computability

1980-06-19
Computability
Author: Nigel Cutland
Publisher: Cambridge University Press
Total Pages: 268
Release: 1980-06-19
Genre: Computers
ISBN: 9780521294652
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What can computers do in principle? What are their inherent theoretical limitations? The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function - a function whose values can be calculated in an automatic way.

Category Theory for Computing Science

1995
Category Theory for Computing Science
Author: Michael Barr
Publisher:
Total Pages: 352
Release: 1995
Genre: Computers
ISBN:
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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.

Basic Category Theory for Computer Scientists

1991-08-07
Basic Category Theory for Computer Scientists
Author: Benjamin C. Pierce
Publisher: MIT Press
Total Pages: 117
Release: 1991-08-07
Genre: Computers
ISBN: 0262326450
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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

An Introduction to Category Theory

2011-09-22
An Introduction to Category Theory
Author: Harold Simmons
Publisher: Cambridge University Press
Total Pages: 237
Release: 2011-09-22
Genre: Mathematics
ISBN: 1139503324
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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.

Theoretical Computer Science for the Working Category Theorist

2022-03-03
Theoretical Computer Science for the Working Category Theorist
Author: Noson S. Yanofsky
Publisher: Cambridge University Press
Total Pages: 148
Release: 2022-03-03
Genre: Mathematics
ISBN: 1108890679
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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.

Categories and Computer Science

1991
Categories and Computer Science
Author: R. F. C. Walters
Publisher: Cambridge University Press
Total Pages: 180
Release: 1991
Genre: Computers
ISBN: 9780521422260
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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.

Category Theory in Context

2017-03-09
Category Theory in Context
Author: Emily Riehl
Publisher: Courier Dover Publications
Total Pages: 273
Release: 2017-03-09
Genre: Mathematics
ISBN: 0486820807
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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.