There are many books designed to introduce category theory to either a mathematical audience or a computer science audience. In this book, our audience is the broader scientific community. We attempt to show that category theory can be applied throughout the sciences as a framework for modeling phenomena and communicating results. In order to target the scientific audience, this book is example-based rather than proof-based. For example, monoids are framed in terms of agents acting on objects, sheaves are introduced with primary examples coming from geography, and colored operads are discussed in terms of their ability to model self-similarity. A new version with solutions to exercises will be available through MIT Press.
arXiv comments
267 pages, 5 chapters, 280 exercises, an index. This book was written as course notes for a special subjects Math class at MIT called "18-S996: Category Theory for scientists", taught in Spring 2013. The class had a diverse enrollment: At the end, the number of registered students was 18 = 7 undergrad + 11 grad = 5 math + 4 EECS + 3 physics + 3 engineering + 3 other
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I have a disclaimer. I'm not an expert in category theory at all. However, my primary background is in mathematics and I've "looked over the basics" as they say. If you'll allow me to dodge the question just a little bit, I'd recommend that you dive in and see what it feels like…
The best way to ensure access to the newest arXiv version is not to link to a specific version at all (and also link to the abstract): https://arxiv.org/abs/1302.6946 . EDIT: But, for no comprehensible reason, Spivak has things set up so that the latest arXiv version is older…
If anyone wants more on categories for non mathematicians be sure to check out David Spivak's work and his book "Category Theory for Scientists" [1]. 1. http://arxiv.org/abs/1302.6946
Here are a few examples. Here's operational transforms from CT [0][1]. Here's probability theory (and thus much of ML) [2][3][4]. Lambda calculus arises as a certain kind of category. Operads form a model for wiring diagrams. Database schemata are categories [5]. [0]…
The Rosetta stone paper: http://math.ucr.edu/home/baez/rosetta.pdf also some preliminaries (books by Simmons, Awodey and Lawvere/Schanuel, spivak): http://arxiv.org/abs/1302.6946 http://www.reddit.com/r/math/comments/1eiyid/category_theory...…
I have a disclaimer. I'm not an expert in category theory at all. However, my primary background is in mathematics and I've "looked over the basics" as they say. If you'll allow me to dodge the question just a little bit, I'd recommend that you dive in and see what it feels like…
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