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Basic Category Theory for Computer Scientists (Foundations of Computing) Paperback – August 7, 1991

by Benjamin C. Pierce (Author)

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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.Contents : Tutorial. Applications. Further Reading.

Basic Category Theory for Computer Scientists (Foundations of Computing)

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Product Details

Series: Foundations of Computing
Paperback: 114 pages
Publisher: The MIT Press; 1 edition (August 7, 1991)
Language: English
ISBN-10: 0262660717
ISBN-13: 978-0262660716
Product Dimensions: 7 x 0.4 x 9 inches
Shipping Weight: 8.8 ounces (View shipping rates and policies)
Average Customer Review: 3.8 out of 5 stars See all reviews (14 customer reviews)
Amazon Best Sellers Rank: #631,420 in Books (See Top 100 in Books)
- #289 in Books > Science & Math > Mathematics > Pure Mathematics > Logic
- #3493 in Books > Computers & Technology > Computer Science
- #8325 in Books > Textbooks > Computer Science

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3.8 out of 5 stars

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Top Customer Reviews

Really expensive for a set of notes...

ByFoo Baron December 6, 2005

Format: Paperback

Now that Barr and Wells have made Category Theory for Computing Science available for free, there's no reason to read anything else. CTCS is an *excellent* intro to category theory, written by actual category theorists.

For more applications to functional programming, try Lambert Meertens, Richard Bird, Oege de Moor, Marten Fokkinga, Jaap Van Oosten, and Roland Backhouse.

For a more mathematical approach, try Eugenia Cheng's excellent videos on YouTube. Or just read MacLane...

22 comments 81 people found this helpful. Was this review helpful to you?YesNo

Too terse

ByA customeron March 27, 2004

Format: Paperback

This is a very short book: 70 pages of text + a bibliography. The first 50 pages are about general category theory, and the last 20 pages are specifically for computer scientists. My interest is in general category theory, and I bought this because I have a BS in CS and thought I'd find plenty of familiar examples. Unfortunately this book doesn't have nearly enough examples. I found it easier to skim some undergrad abstract algebra books in the library (groups, rings, vector spaces) and then continuing with category theory intros written for math students.

0Comment 38 people found this helpful. Was this review helpful to you?YesNo

Basic crib sheet for category theory

ByJ. Elliotton April 2, 2006

Format: Paperback

Anyone coming to this book from Pierce's "Types and Programming Languages" will be disappointed. While his "Types ..." book is a model of clear exposition, this book reads like a set of notes jotted down on the back on an envelope. The extensive bibliographic sections are more than fifteen years out of date. Much of the material referenced is no longer in print, and recent developments are, of course, not mentioned. Those seeking a very gentle introduction to category theory would do better with the book by Lawvere and Schanuel, who cover more of category theory than Pierce. Mathematically mature computer science readers will find everything they need to know about the subject in Mac Lane's book.

0Comment 24 people found this helpful. Was this review helpful to you?YesNo

Clear and concise

ByMJRon December 12, 2001

Format: Paperback

This is an excellent introduction to category theory, not just for computer scientists, but for mathematicians as well. The author has a very clear writing style--it's evident that he writes to help people to understand the subject, and not to show off his knowledge. The examples illustrating various principles are easy to understand, especially the ones used to illustrate adjoints, arguably one of the more difficult concepts in category theory. This book also comes with a very valuable annotated bibliography, enabling one to intelligently choose from the many books and articles in this burgeoning field.
Read this book before you tackle Mac Lane.

0Comment 21 people found this helpful. Was this review helpful to you?YesNo

The first 2 chapters give a good overview of the subject

ByDavid Arpon August 28, 2015

Format: PaperbackVerified Purchase

The first 2 chapters give a good overview of the subject. The third chapter is on applications of the theory to computer science, esp. the lambda calculus, which was beyond me and not well written. Would recommend this book despite its shortcomings. Make sure to do the exercises in the first 2 chapters. Should supplement book with the wikipedia article on adjoint functors.

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A Good Read

ByJason Dusekon August 24, 2008

Format: Paperback

This book is not exactly what I would call easy going. I've managed to get through half of it in 7 months. However, I can say, with absolute confidence, that if you do the problems you will learn.

Most everything I've seen on category theory is a confusing mixture of different notations with seemingly identical meanings (but in fact the meanings are totally different). This book is no exception. Often, I have resorted to IRC to sort things out when some notation is simply impenetrable to me. My mathematical training stopped at complex calculus, so this may not apply to you if you've had abstract algebra or something a little more 'meta'.

There seems to be one typographical error, but I am not sure. In the example on the adjunction between products and exponentiation, the right adjoint is listed as "(_)^A x A" but in the diagrams it ends up as "(_)^A". This may be a sensible ellision, but it is not explained anywhere in the text and of it's not easy to find these things on the internet.

0Comment 3 people found this helpful. Was this review helpful to you?YesNo

nice and slim (the text is only ~70 pages)!

ByKing Yin Yanon October 2, 2010

Format: Paperback

I'm still a beginner at category theory, but I'd like to say this is a nice textbook. The examples are easy to follow (mainly basic set theory), for people with a com sci background.

A later section explains CCCs (Cartesian closed categories) and its isomorphism to typed lambda calculus. I don't fully grasp the details but this is a very important result in higher-order logic, particularly because the substitution mechanism of lambda calculus can be modeled by category theory.

0Comment 3 people found this helpful. Was this review helpful to you?YesNo

Most Recent Customer Reviews

Good book to have on-hand for reference

I've very much enjoyed this book but have found that it doesn't do the best job of clearly delineating the abstract categorical interpretation from whatever (semi)concrete...Read more

Published 8 months ago by Amazon Customer

I feel cheated and disappointed with amazon

I can't read it in my kindle nor in the cloud, I feel cheated and disappointed with amazon.

Published 9 months ago by mbuceta

Concise and not too difficult

Dr. Pierce's style is a little informal compared to pure math books like Mac Lane's "Categories for the Working Mathematician", but I enjoy that more relaxed style of writing when...Read more

Published on March 21, 2014 by hans

The best category book so far targeting programmers, not mathematicians

I recommend this book to everyone; we did cover it a while ago at our BACAT meetup, and now are doing it again (for new participants), working on exercises, etc.Read more

Published on July 8, 2013 by vpatryshev

Good stuff on the matter

Author doing his best to explain category theory in terms of discrete math. Gives much more broader look, than all of the articles on this theme I've read.

Published on October 26, 2011 by Arttu

Good Introduction

I have been reading several different category theory texts recently, and this one was very succinct and accessible. Particularly useful for understanding functional programming.

Published on February 20, 2007 by grrdo

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