Category Theory for the Sciences

by David I. Spivak

An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences. Category theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in monoids, groups, orders, and graphs—categories in disguise. After explaining the “big three” concepts of category theory—categories, functors, and natural transformations—the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions. Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.

Genres: Mathematics, Science, Nonfiction, Textbooks

486 pages, Hardcover

First published February 27, 2013

Reviews

[Zarathustra Goertzel · Rating 4 out of 5]

A really good basic introduction to category theory.
The book focuses on giving you an intuitive and practical understanding of category theory, which is exactly what one wants come from Haskell (err, computer science). It does this by being 2/3 examples and excersises (mostly with solutions) elucidating the key concepts.
Of course, all but a handfull of propositions also have proofs.

[Mark Moon · Rating 3 out of 5]

I didn't think the category theory material was well-organized. The examples and problems seemed to be very eclectically-chosen, and many had typos. There were some nice applications at the end, but not as many as I would have liked in the rest of the text.

[Christopher Conrad · Rating 2 out of 5]

Pointless, does not share the essence of category theory in the least bit. I really do not understand why an attempt to water down and trivialize the ideas of category theory is published.

[George · Rating 4 out of 5]

Full review at https://constantinides.net/2019/12/09...

[Marek Krajewski · Rating 2 out of 5]

Sorry, didn't finished it, but not because it's too boring - I just haven't got time for it at one moment, and then never managed to pick up reading again.

The material is OK, but I failed to be excited about category theory as I was (time ago) about set theory or logic. Still waiting for that book.

That's not saying the book is bad, but that my expecttactions were different.

[Jiaming Jiang · Rating 4 out of 5]

Very good introduction to the basic concepts (including Yoneda Lemma) in category theory, with extensive applications in algebra and database. But some definitions are stated in terms of sets rather than a more generic notion. One who has never been exposed to category theory may need to refer to more well-recognized and more general definitions, such as the ones found in Wikipedia.

[Stephen Lee · Rating 3 out of 5]

I checked this out after skimming Wikipedia pages and professor's notes over a long period of time (being a Haskell programmer), and I don't feel I've learned much after reading it. I continued with another book, Tom Leinster's, that goes into less material (no monads, operads, etc.) but motivates and explains the matter in a more down to earth way.

[Chu Pi · Rating 5 out of 5]

Enthusiastically written!
It can be said to be an unified framework for scientific discoveries.

The only thing that still struggles me after reading this book is: what does it feel being a category (or not a category?)

[G]

I could not see the value I would gain from learning that much math.
It may be there, but I did not buy in.