Category Theory for the Sciences

Category theory was invented in the 1940s to unify and synthesize different areas inmathematics, and it has proven remarkably successful in enabling powerful communication betweendisparate fields and subfields within mathematics. This book shows that category theory can beuseful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout thesciences. Information is inherently dynamic; the same ideas can be organized and reorganized incountless ways, and the ability to translate between such organizational structures is becomingincreasingly important in the sciences. Category theory offers a unifying framework for informationmodeling that can facilitate the translation of knowledge between disciplines. Written in anengaging and straightforward style, and assuming little background in mathematics, the book isrigorous but accessible to non-mathematicians. Using databases as an entry to category theory, itbegins with sets and functions, then introduces the reader to notions that are fundamental inmathematics: monoids, groups, orders, and graphs -- categories in disguise. After explaining the"big three" concepts of category theory -- categories, functors, and naturaltransformations -- the book covers other topics, including limits, colimits, functor categories,sheaves, monads, and operads. The book explains category theory by examples and exercises ratherthan focusing on theorems and proofs. It includes more than 300 exercises, with selected solutions.Category Theory for the Sciences is intended to create a bridge between the vastarray of mathematical concepts used by mathematicians and the models and frameworks of suchscientific disciplines as computation, neuroscience, and physics.

David I. Spivak is a Research Scientist in the Department of Mathematics at MIT.