Sheaf Theory through Examples (Abridged Version)

TL;DR

This book offers an accessible introduction to sheaf theory through numerous concrete examples and applications, making complex concepts approachable for newcomers and emphasizing applied category theory.

Contribution

It uniquely combines applied category theory with practical examples to teach sheaf theory to a less specialized audience, including new advanced topics in the extended version.

Findings

Broad range of applications demonstrated

Concrete constructions facilitate understanding

Extended chapter on advanced topics included

Abstract

This book provides an inviting tour through sheaf theory, from the perspective of applied category theory and pitched at a less specialized audience than is typical with introductions to sheaves. The book makes it as easy as possible for the reader new to sheaves, by motivating and developing the theory via a broad range of concrete examples and explicit constructions, including applications to n-colorings of graphs, satellite data, chess problems, Bayes nets, musical performance, complexes, and more. Included is an extended first chapter introducing and motivating all the necessary category-theoretical background, again with a strong emphasis on concrete examples. A new and unabridged version (including a fifth chapter on more advanced topics and a conclusion) will be available with MIT Press.