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 Title Category Theory for the Sciences
 Author(s) David I. Spivak
 Publisher: The MIT Press; 1 edition (October 10, 2014)
 License: AttributionNoncommercialShare Alike 3.0
 Hardcover 496 pages
 eBook PDF, ePub, Mobi (Kindle), etc.
 Language: English
 ISBN10/ASIN: N/A
 ISBN13: 9780262028134
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Book Description
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 nonmathematicians.
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.
About the Authors David I. Spivak is a research scientist in the mathematics department at MIT. His current research is on Categorical Informatics, i.e. using category theory to study information as it is used in the world. Previous research subjects include Derived Manifolds, Infinity categories (a.k.a. quasicategories), and Physics.
 Category Theory
 Applied Mathematics
 Graph Theory
 Algebra, Abstract Algebra, and Linear Algebra, etc.
 Functional Programming and Lambda
 Database Theory and Systems
 Category Theory for the Sciences (David I. Spivak)
 2013 Edition  PDF (267 pages) [Mirror]
 Book Homepage
 An Invitation to Applied Category Theory: Seven Sketches in Compositionality
 Basic Category Theory (Tom Leinster)
 Category Theory in Context (Emily Riehl)
 Category Theory for Programmers (Bartosz Milewski)
 Categories, Types, and Structures (Andrea Asperti, et al)
 Type Theory and Functional Programming (Simon Thompson)
 Programming in MartinLof's Type Theory: An Introduction (Bengt Nordstrom, et al)