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Conceptual Mathematics: A First Introduction to Categories 1st Edition

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F. William Lawvere (Author)
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F. William Lawvere (Author), Stephen Hoel Schanuel (Author)
4.1 out of 5 stars 16 customer reviews
ISBN-13: 978-0521478175
ISBN-10: 0521478170
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Conceptual Mathematics: A First Introduction to Categories
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Product Details

  • Paperback: 376 pages
  • Publisher: Cambridge University Press; 1st edition (November 28, 1997)
  • Language: English
  • ISBN-10: 0521478170
  • ISBN-13: 978-0521478175
  • Product Dimensions: 6.8 x 1.1 x 9.7 inches
  • Shipping Weight: 1.4 pounds
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (16 customer reviews)
  • Amazon Best Sellers Rank: #144,713 in Books (See Top 100 in Books)

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5.0 out of 5 starsInteresting and Accessible at Many Levels
By A Customer on August 2, 1998
Format: Paperback
Lawvere and Schanuel have created a book at once accessible and stimulating at a great many levels. It discusses the concepts of Category Theory in a simulated "classroom" setting, addressing common questions of students at crucial points in the book. It also wanders in a care-free manner through an amazing number of topics. The book is interesting to non-mathematicians at a philosophical level, and to (beginning) mathematicians as an introduction to an exciting new area of mathematics. The authors have a great attitude, and offer great starting-points for investigation.
I read it as a first year pure math undergraduate, and though it was at times at too low a level (the 'tests,' for instance, are very easy reviews of basic ideas), it never became boring. For me, it read 'like a novel' (and a page-turner, at that). My only gripe is the lack of an annotated "further reading" section, which would have rounded out the book.
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4.0 out of 5 starsGreat book; whether you should read it depends on you
By Chris Smith on November 30, 2006
Format: Paperback
Many of the reviews evaluate the book from the perspective of graduate students in mathematics want to learn categories, and it's certainly the wrong choice for that purpose. If you think of this as a serious math textbook, then it fails in that goal: significant proofs are the exception rather than the rule; very few, and trivial, exercises; very lacking in depth.

This is a great book because it provides a motivation for investigating categories. It helped me when I was in the position of hearing from a lot of places that subjects I was interested in often used category theory. I tried to read a few "real" books about category theory, and didn't get very far because they did not make the connections I was looking for. I accumulated three or four such books, all with bookmarks at about page 50 to 75. This book taught me relatively little about the theory of categories or the body of knowledge about them, but it provided a wealth of connections between categories and other topics, which made me better able to finish a couple of the real books and figure out what I needed to know there.

My advice, if you're in anything like that situation, is to read this book. Just don't take it too seriously, and don't try to milk more out of it than is really there. Then go learn more about category theory from elsewhere.
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5.0 out of 5 starsIntuitive Introduction
By A Customer on June 6, 2000
Format: Hardcover Verified Purchase
Highly intuitive introduction to this abstract, but highly practical area of mathematics with one glaring fault. First the good news. I have never seen a more carefully explained introduction into an area of mathematics. Many examples and explanations of the principles behind and applications of concept analysis. However, the glaring fault is organization. Details are given without adequate tie in to how they relate to others. The text bounces from one area to the next so it is easy to lose sight of the whole picture. On balance its strengths far outweigh its weaknesses so I recommend it without reservation.
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5.0 out of 5 starsOustanding book: an absolute must-read for any mathematician
By Alexander C. Zorach on October 21, 2006
Format: Paperback
In the preface of this book, the author comments that this book has been used successfully in high schools, colleges, graduate schools, and by professors. After reading this book, I can believe it. This book is simply a gem.

Mind you, although this book is very easy to read, some of the concepts contained within it are very abstract and can be very difficult to fully comprehend. While a high school student will surely get something out of this book, it would be hard to understand everything in it without knowing a fair amount of mathematics.

I would recommend this book to any mathematician. It is an absolute must-read. The author makes the claim that working through this book will improve your ability to categorize (no pun intended!) your mathematical knowledge so as to better know how to approach problems. From my experience, this claim is true. This book somehow teaches some of the things about problem-solving that many people believe cannot be taught.

This book looks deceptively simple, especially relative to beasts such as MacLane's "Categories for the Working Mathematician". However, I find that I keep coming back to this book, sometimes after several months. In particular, I have found that reading this book has opened the door to understanding some of the advanced mathematics books that previously seemed inaccessible to me, such as Lang's "Algebra".
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2.0 out of 5 starsA Good Introduction
By Elias F Ponvert on November 8, 2001
Format: Paperback
As a first introduction to Categories, this book is well written, clever, simple and very clear. However, I was disappointed with it. From the notoriety of the authors and the, yes, cool illustrations I assumed it would be a gem. However, it fell short. I've been toying with Category Theory for a few years, and every time I try to get into a book on Categories I get stumped at the notions of Functors and Natural Transformations. This book, however, dealt with neither at length, despite the fact that Category Theory originated around the notion of Natural Transformations in the first place. (As I understand it at least.) That said, there are many very cool passages in the book, including a functional analysis of a Chinese restaurant and an elegent exposition of Brouwer's Fixed Point Theorem.
Still, for my purposes, I prefer Robert Goldblatt's "Topoi: The Categorical Analysis of Logig" and Michael Barr's "Category Theory for Computing Science". As both are intended for non Category Theorists, both build their presentations of Category Theory from sratch. Sadly, I think both are out of print. Not for the faint of heart, I'm told Saunders Mac Lane's "Categories for the Working Mathematician" is the classic. (It's on my wish list.)
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Most Recent Customer Reviews

5.0 out of 5 starsWould recommend to anyone

Would recommend to anyone. Amazing author, clear and interesting explanation. He lacks the pervasive overblown quality I find in most mathematicians (most academicians, really)...

Published 23 months ago by A. Landreau
4.0 out of 5 starsLight Introduction Only

The introduction alerts the reader that this book is pitched to an audience that includes *high school* readers. Read more

Published on March 19, 2010 by Customer
5.0 out of 5 starsExcellent Introduction

I've been interested in category theory for many years, and I have several books on it. This is the first book that is truly an introduction to categorical thinking. Read more

Published on August 14, 2008 by J. V. White
5.0 out of 5 starsOne Star? Such a Generous Heart!!

When I saw the one star review, and the general disagreement about the merits of this book I couldn't help but jump in. Read more

Published on August 7, 2008 by William D. Fusfield
5.0 out of 5 starsExcellent, as far as it goes

The theoretical physicist John Baez wrote, "[Conceptual Mathematics] may seem almost childish at first, but it gradually creeps up on you. Read more

Published on June 20, 2008 by Amazon Customer
4.0 out of 5 starsnot a book for self study

I bought this book a year ago and use it to teach myself the basics. it is difficult to go thru the exercises and tests because no answers are given, and at this stage of... Read more

Published on April 17, 2006 by Ronald Woode
5.0 out of 5 starsObjects and maps are everywhere

Excellent book for non-professional mathematicians, like me (I'm a software engineer), who wants to understand modern mathematics and apply its ideas in analysis of complex... Read more

Published on June 21, 2004 by Dmitry Vostokov
3.0 out of 5 starsVery uneven, but still useful

As a topic in itself, category theory should need not to wait until grad-level to be described just because that may be when category theory's power can really begin to be... Read more

Published on November 10, 2002 by T. Gwinn
1.0 out of 5 starsHeavy Hitter Strikes Out

I sure hope Schanuel wrote this book and the publisher simply tacked on
Lawvere's name for marketing purposes. Read more

Published on October 20, 2002 by kal@kalx.net
3.0 out of 5 starsA retract in search of a section

There is a wonderful course in category theory for high school students, just begging to be excavated from this multi-layered book. Read more

Published on March 20, 2002 by William E. Margolis

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