Category Theory for the Sciences by David I. Spivak
Category Theory for the Sciences by David I. Spivak PDF, ePub eBook D0wnl0ad
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 solutions. Category Theory for the Sciences 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.
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