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21 of 25 people found the following review helpful
5.0 out of 5 stars Clear and concise
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...
Published on December 12, 2001 by Michael Rosenborg

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65 of 68 people found the following review helpful
1.0 out of 5 stars Really expensive for a set of notes...
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...
Published on December 6, 2005 by Foo Bar


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65 of 68 people found the following review helpful
1.0 out of 5 stars Really expensive for a set of notes..., December 6, 2005
By 
Foo Bar (United States) - See all my reviews
This review is from: Basic Category Theory for Computer Scientists (Foundations of Computing) (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...
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35 of 38 people found the following review helpful
3.0 out of 5 stars Too terse, March 27, 2004
By A Customer
This review is from: Basic Category Theory for Computer Scientists (Foundations of Computing) (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.
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21 of 22 people found the following review helpful
2.0 out of 5 stars Basic crib sheet for category theory, April 2, 2006
By 
J. Elliott (Natick, MA USA) - See all my reviews
(REAL NAME)   
This review is from: Basic Category Theory for Computer Scientists (Foundations of Computing) (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.
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21 of 25 people found the following review helpful
5.0 out of 5 stars Clear and concise, December 12, 2001
By 
Michael Rosenborg (Canyonville, OR USA) - See all my reviews
(REAL NAME)   
This review is from: Basic Category Theory for Computer Scientists (Foundations of Computing) (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.
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3 of 3 people found the following review helpful
5.0 out of 5 stars nice and slim (the text is only ~70 pages)!, October 2, 2010
By 
King Yin Yan (Lantau, Hong Kong) - See all my reviews
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This review is from: Basic Category Theory for Computer Scientists (Foundations of Computing) (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.
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2 of 2 people found the following review helpful
4.0 out of 5 stars A Good Read, August 24, 2008
By 
Jason Dusek (San Francisco, CA USA) - See all my reviews
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This review is from: Basic Category Theory for Computer Scientists (Foundations of Computing) (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.
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1 of 1 people found the following review helpful
4.0 out of 5 stars Concise and not too difficult, March 21, 2014
By 
hans (State College, PA USA) - See all my reviews
This review is from: Basic Category Theory for Computer Scientists (Foundations of Computing) (Paperback)
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 I am first learning a field.

The biggest obstacle for learning category theory is the fact that category theory generalizes a lot of areas of pure mathematics like topology, abstract algebra, and geometry. It's hard to generalize before you have examples to generalize, but the examples being generalized in category theory are mostly from higher level mathematics found in senior level undergraduate and graduate level courses. Pierce ameliorates this problem by introducing some of the most basic categories first: sets, ordered sets, partially ordered sets, groups, monoids, vector spaces, measure spaces, topological spaces, proofs, and a simple functional computer language. He takes the time to explicitly define most of these ideas, so, in theory, you could read this book without a background in theoretical mathematics, but it would be hard.

After defining categories and introducing the most basic categories, Pierce describes and defines the most basic ideas in category theory: subcategories, commutative diagrams, monomorphisms, epimorphisms, isomorphisms, initial/terminal objects, products, coproducts, universal constructions, equalizers, pullbacks, pushouts, limits, cones, colimits, cocones, exponentiation, and closed Cartesian categories. These ideas are spelled out over the thirty pages of chapter one including illuminating homework exercises. The homework exercises varied significantly in difficulty. Many of the exercises were trivial and there are two or three that I am still working on despite investing several hours of thought. Generally, I found the exercises to be a bit harder than those in Mac Lane's book, but Pierce's book required less of a background in mathematics. A couple of the exercises were incorrectly stated or impossible.

Chapter two introduced functors, natural transformations, adjoints, and F-algebras. After reading this chapter, I was finally able to understand the definition of monads which are an important part of the computer language Haskell! Pierce provides many examples of each of these ideas and enjoyable homework exercises to increase understanding. Pierce's definition of adjoints is much easier to understand than the standard definitions using counit adjunction or Hom Sets.

The last major chapter concerns applications of category theory to computer science-specifically lambda-calculus and programming language design.

The first two chapters of the book give a reasonable, condensed introduction to category theory for students that have taken a course in abstract algebra. A course in topology or linear algebra would be another useful prerequisite. I carried around the light 100 page book for a few months so that I could learn something whenever I had some extra time. I had hoped that when I had proven that several functors where monads, I would then really understand monads, but a full understanding still eludes me. Similarly, I had proven that several functor pairs are adjoint, but even after I finished the book, I did not feel as though I understand adjoint functors. I had to read a few other sources and the Wikipedia before I felt comfortable with adjoints.

In summary, it's a nice, concise introduction to category theory that almost does not require a graduate level understanding of mathematics.

A slightly different version of this review appeared in my blog at artent.net.
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1 of 1 people found the following review helpful
5.0 out of 5 stars Good stuff on the matter, October 26, 2011
Verified Purchase(What's this?)
This review is from: Basic Category Theory for Computer Scientists (Foundations of Computing) (Paperback)
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. Price is high, though, but I guess, sometimes you can make such an investment in your knowledge of computer science.
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9 of 14 people found the following review helpful
5.0 out of 5 stars This book is a CCC., October 11, 2001
By A Customer
This review is from: Basic Category Theory for Computer Scientists (Foundations of Computing) (Paperback)
Which stands for "Compact, Complete, and Comprehensible".
It is fairly easy to read, has every basic aspects of Category Theory, and has a lot of good examples.
If you would like to know the first step of Category Theory and you are in CS realm, this book is the one you have to try.
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3 of 5 people found the following review helpful
4.0 out of 5 stars Good Introduction, February 20, 2007
By 
grrdo (Toronto, Canada) - See all my reviews
This review is from: Basic Category Theory for Computer Scientists (Foundations of Computing) (Paperback)
I have been reading several different category theory texts recently, and this one was very succinct and accessible. Particularly useful for understanding functional programming.
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Basic Category Theory for Computer Scientists (Foundations of Computing)
Basic Category Theory for Computer Scientists (Foundations of Computing) by Benjamin C. Pierce (Paperback - August 7, 1991)
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