A Gentle Introduction to Category Theory
~ Maarten M Fokkinga
Details
Year of publication
1992
Editor
University of Utrecht
Description
In these notes we present the important notions from category theory. The intention is to provide a fairly good skill in manipulating with those concepts formally. What you probably will not acquire from these notes is the ability to recognise the concepts in your daily work when that differs from algorithmics, since we give only a few examples and those are taken from algorithmics. For such an ability you need to work through many, very many examples, in diverse fields of applications.
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Categories, Types, and Structures: An Introduction to Category Theory for the Working Computer Scientist (Foundations of Computing Series)
by: Andrea Asperti, Giuseppe Longo
Details
# Hardcover: 320 pages
# Publisher: The MIT Press (August 23, 1991)
# Language: English
# ISBN-10: 0262011255
# ISBN-13: 978-0262011259
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. "Categories, Types and structures" provides a self-contained introduction to general category theory and explains the mathematical structures that have been the foundation of language design for the past two decades. The authors observe that the language of categories could provide a powerful means of standardizing of methods and language, and offer examples ranging from the early dialects of LISP, to Edinburgh ML, to work in polymorphisms and modularity. The book familiarizes readers with categorical concepts through examples based on elementary mathematical notions such as monoids, groups and toplogical spaces, as well as elementary notions from programming-language semantics such as partial orders and categories of domains in denotational semantics. It then pursues the more complex mathematical semantics of data types and programs as objects and morphisms of categories.
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From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory (Logic, Epistemology, and the Unity of Science)
by: Jean-Pierre Marquis
Details
# Hardcover: 320 pages
# Publisher: Springer; 1 edition (December 5, 2008)
# Language: English
# ISBN-10: 1402093837
# ISBN-13: 978-1402093838
Description
From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein s Erlangen program in geometry is in fact a particular instance of a general and broad phenomenon revealed by category theory. The volume starts with Eilenberg and Mac Lane s work in the early 1940 s and follows the major developments of the theory from this perspective. Particular attention is paid to the philosophical elements involved in this development. The book ends with a presentation of categorical logic, some of its results and its significance in the foundations of mathematics.
From a Geometrical Point of View aims to provide its readers with a conceptual perspective on category theory and categorical logic, in order to gain insight into their role and nature in contemporary mathematics. It should be of interest to mathematicians, logicians, philosophers of mathematics and science in general, historians of contemporary mathematics, physicists and computer scientists.
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Basic Category Theory for Computer Scientists (Foundations of Computing)
by: Benjamin C. Pierce
Details
# Paperback: 114 pages
# Publisher: The MIT Press; 1 edition (August 7, 1991)
# Language: English
# ISBN-10: 0262660717
# ISBN-13: 978-0262660716
Description
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.
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