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.
