Category Theory for the Sciences
David I. Spivak
The MIT Press
<P>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 mathematics: 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 selected solutions. <I>Category Theory for the Sciences</I> 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.</P>