Category Theory for the Sciences (David I. Spivak)

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Category Theory for the Sciences (David I. Spivak)

In order to unite and synthesize many areas of mathematics, category theory was developed in the 1940s, and it has proven to be extremely effective at fostering effective communication between diverse subjects and subfields of mathematics.

This book demonstrates how category theory can be used in the sciences as a rigorous, adaptable, and cohesive modeling language. The capacity to translate between different organizational structures is becoming more and more crucial in the sciences since information is essentially dynamic and may be structured and reorganized in endless ways.

A unified framework for information modeling provided by category theory can aid in the transfer of knowledge between disciplines. The book is rigorous but understandable to non-mathematicians since it is written in an interesting and easy manner and assumes little prior knowledge of mathematics.

It starts with sets and functions before introducing the reader to concepts that are basic to mathematics, such as monoids, groups, orders, and graphs, which are actually categories in disguise. The book goes through other topics including limits, colimits, functor categories, sheaves, monads, and operads after explaining the "main three" notions of category theory: categories, functors, and natural transformations.

Instead of concentrating on theorems and proofs, the book illustrates category theory through examples and activities. More than 300 exercises with solutions are included.

The goal of this book is to build a bridge between the enormous variety of mathematical ideas employed by mathematicians and the models and conceptual frameworks utilized in fields like computer, neuroscience, and physics.

Ebook Details

About the Authors
At MIT, David I. Spivak works as a research scientist in the mathematics division. His current work focuses on categorical informatics, which uses category theory to examine how people use information in the real world. Derived Manifolds, Infinity categories (also known as quasi-categories), and Physics have all been the topic of prior investigation.
Published Date / Year
1 edition (October 10, 2014)
Attribution-Noncommercial-Share Alike 3.0
496 pages
eBook Format
HTML, PDF, ePub, Mobi (Kindle), etc.

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