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rxs comments on Open thread, May 17-31 2013 - Less Wrong Discussion
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Comments (311)
Category theory gives a few hits at LW, but doesn't seem to be recognized very wildly. On a first glance it seems to be relevant for Bayes nets, cognitive architectures and several other topics. Recent text book that seems very promising:
Category theory for scientists by David I. Spivak: http://arxiv.org/abs/1302.6946
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.
These texts can work as an introductory undergraduate sequence (with "Sets for Mathematics" going after enough exposure to rigor, e.g. a real analysis course, maybe some set theory and logic, and Awodey's book after a bit of abstract algebra, maybe functional programming with types, as in Haskell/Standard ML/etc.):
Second the recommendation of Lawvere and Schanuel. It really communicates the categorical way of thinking without requiring a lot of mathematical background (more traditional texts on category theory will talk about things like algebraic topology which historically motivated category theory but aren't conceptually prior to it).