Category Theory for the Sciences (Mit Press)

David Spivak is a welcome new breed of MIT lecturer whose passion is to motivate, engage, and facilitate a students learning of a subject.Its predecessors are "Category Theory for Computer Scientists" Barr & Wells, "A First Introduction to Categories" - Lawvere & Schnauel, and"Category Theory" -Awodey. This book is a Rosetta Stone for understanding the forthcoming new applications of Category Theory to real world issues such as the foundations of computer science (e.g., Algebraic Theory of Machines - Jack Rhodes and Ken Khon) and physics ( e.g., John Baez).Where was Spivak when one first encountered the new and ethereal Category Theory in the late 1950's under Dan Kan, Warren Ambrose, andSerge Lang. Closest comparison would be BUD/S training.And let us not forget the esteemed George Whitehead classes ( e.g. "Elements of Homotopy Theory"which was based on his lectures ): --- Enter the class room; start writing as fast as possible on the blackboard mimicking tap-dancing squirrels, andwhen reaching the end of the blackboards erasing the first board. Carpal Tunnel Syndrome for the few survives of his course.As with Barr & Wells, Spivak supplies answers that facilitate grasping the underlying metaphors of the subject presented with instant feedbackallowing a natural progression of the subject. He smoothly inculcates the reader with the metaphors for further study such as Grothendieck Construction and Topos theory. Peter T. Johnstone's Olympian "Topos Theory " (Dover) and "Sketches of an Elephant" are the ultimate injoyous reading for the mathematically 'deranged' who cannot get enough.Only one kvetch. The printing of the text is so light that one wonders if MIT Press had run out of toner, making reading a chore for older readers.In contrast, Norbert Wiener's "Cybernetics 2", 1960 is still readable because real ink was used.In conclusion Spivak's book is a joy and an important gateway for a scientist of the new emerging fields.

Pros:* Has lots of examples/questions with solutions, which help you clearly understand the concepts being discussed,* Spivak builds up concepts gradually with lots of worked out examples,* Requires little by way of mathematical background. Very suitable for non-mathematicians or those with basic mathematical background.* An early version is available online in PDF format, so you can evaluate before buying. The book contains solutions after every "exercise", not so for the PDF.Cons:* Much of the early part of the book is motivated by "ologs", which I feel have doubtful utility in practical science. I feel this detracts from the overall presentation.* The book takes a long time to actually introduce Categories, because Spivak takes the time to introduce mathematical background. However, this forces the reader wade through a lot of material, which is likely unfamiliar to his target audience and -- I feel -- is less useful in actually understanding Category theory. Overall, I found this "bottom-up" pedagogical approach makes it quite hard to see the forest (broad ideas & thrust of category theory) for the trees (a multitude of newly introduced concepts).I gave up reading Spivak after Chapter 3 and switched to Awodey's excellent Category Theory book. Awodey's approach is "top-down", introducing categories almost immediately then examples to flesh out the concepts. It has a far more abstract and intuitive flavor in its presentation compared to Spivak, which is what I like most about it. However, it is also much denser than Spivak, and is a far more challenging read, but should still be accessible to anyone with first year college-level exposure to abstract algebra.

This will be short and to the point, rather different from Mr. Spivak's book. First, I think it is a very good book if you want to see why category theory is useful in computer science. It is not a very good book if you want to learn category theory in general, because it is CLUTTERED with too much, well, clutter, between the actual definitions and theorems. But there are flashes of brilliance in the exposition and it is probably worth the slog through the clutter. A worthwhile effort.( And I agree with another reviewer that "ologs" are not worth all the space Spivak gives them. I think they really add nothing much and might better be a quick aside in the section on databases.)

This book is one of kind, the only one for readers of none mathematical background. It of course still takes quite an effort to learn CT from this book. I have a Ph. D. in engineering and had some advanced algebraic and analytic math courses during my college years. So far I only understand the very basic part of the CT. The higher category and natural transformation part are still out of my reach. I won't blame to author for that. I don't have the complete prerequisite. I hope some day I will get to it.Despite of that, I have benefited a lot from the learning in my current professional endeavor. It helps me sort out the complex domain problems more clearly. I hope there is a better way of complaining the math, but it may be something not at attainable.

A little hard to get through at first, as the descriptions of his fundamental concept, ologs, was both wordy and a bit obtuse. But htis is ground breaking in its relationship to the use in computation and that is a big deal. By itself it may not be sufficient to grasp all the essentials of category theory and thus Suanders MacLane's Mathematics Form and Function is still the best overall overview

The content is great, but the paper is so thin that its almost transparent so we see the other side which is really visually noisy, annoying. Dont even think using high-lighters on these.. unless you like to see clearly visible line on the other side of the page.Also why a rigid cover? So you can raise the price for no reason? At least drop the rigid cover and make paper that really matter - the one showing the content - a decent thickness/quality..

I decided that I needed a formal category theory background when trying to understand typeclasses in Haskell. This book perfectly serves the aim, introducing the theory in a formal yet not too abstract way. The application to databases and ologs is nice.The book has a formal structure of a mathematical text (definitions, propositions, theorems, however often without a proof) and a lot of examples.Has a minor drawback though, namely a relatively high density of typos, but I guess it's a common first edition symptom.

A very accessible and informative book on broad applications of category theory. Especially useful in information technology modelling

This book is useful for SIMULINK and MySQL modeling.