Category Theory for Scientists by David Spivak.
Abstract:
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.
I first saw this at: Category Theory for Scientists by John Baez.
I forwarded it to Jack Park who responded with a link to an earlier post: Spivak on Category Theory by Bruce Bartlett.
David Spivak responds to the earlier post with a link to a Google doc for posting comments:
CT4S book: Typos, comments, questions, and suggestions
The MIT course description with links to supplemental materials: 18-S996, Spring 2013: Category theory for scientists.
If you post about this book, please include a pointer to the Google doc for comments as well.