Seven Sketches in Compositionality: An Invitation to Applied Category Theory

TL;DR

This book introduces advanced category theory concepts through seven real-world applications, providing accessible sketches that connect practical examples like databases and circuits with categorical structures.

Contribution

It offers a gentle, introductory exploration of complex categorical ideas via concrete examples, making advanced topics accessible without prior knowledge.

Findings

Illustrates categorical structures in real-world contexts

Provides a beginner-friendly tour of advanced category theory topics

Connects applications like databases and circuits with theoretical concepts

Abstract

This book is an invitation to discover advanced topics in category theory through concrete, real-world examples. It aims to give a tour: a gentle, quick introduction to guide later exploration. The tour takes place over seven sketches, each pairing an evocative application, such as databases, electric circuits, or dynamical systems, with the exploration of a categorical structure, such as adjoint functors, enriched categories, or toposes. No prior knowledge of category theory is assumed. A feedback form for typos, comments, questions, and suggestions is available here: https://docs.google.com/document/d/160G9OFcP5DWT8Stn7TxdVx83DJnnf7d5GML0_FOD5Wg/edit