Category theory for scientists (Old version)

TL;DR

This book introduces category theory to a broad scientific audience, emphasizing practical examples and applications across various sciences to demonstrate its usefulness as a modeling and communication framework.

Contribution

It presents category theory in an accessible, example-based manner tailored for scientists outside pure mathematics or computer science.

Findings

Category theory can model phenomena across sciences.

Examples include monoids, sheaves, and operads in real-world contexts.

The approach facilitates interdisciplinary understanding and communication.

Abstract

There are many books designed to introduce category theory to either a mathematical audience or a computer science audience. In this book, our audience is the broader scientific community. We attempt to show that category theory can be applied throughout the sciences as a framework for modeling phenomena and communicating results. In order to target the scientific audience, this book is example-based rather than proof-based. For example, monoids are framed in terms of agents acting on objects, sheaves are introduced with primary examples coming from geography, and colored operads are discussed in terms of their ability to model self-similarity. A new version with solutions to exercises will be available through MIT Press.