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Category Theory for the Sciences (Hardcover)
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Category Theory for the Sciences (Hardcover)
Series: Category Theory for the Sciences
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An introduction to category theory as a rigorous, flexible, and
coherent modeling language that can be used across the sciences.
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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