Basic Category Theory

TL;DR

This introductory textbook on basic category theory explains core concepts like universal properties, adjoint functors, and limits with numerous examples, aimed at readers with limited mathematical background.

Contribution

It provides a clear, example-rich introduction to fundamental category theory concepts, including detailed explanations of complex ideas like the Yoneda lemma.

Findings

Comprehensive coverage of universal properties and their expressions.

Extensive examples from various mathematical areas.

Detailed explanations of advanced concepts like the Yoneda lemma.

Abstract

This short introductory category theory textbook is for readers with relatively little mathematical background (e.g. the first half of an undergraduate mathematics degree). At its heart is the concept of a universal property, important throughout mathematics. After a chapter introducing the basic definitions, separate chapters present three ways of expressing universal properties: via adjoint functors, representable functors, and limits. A final chapter ties the three together. For each new categorical concept, a generous supply of examples is provided, taken from different parts of mathematics. At points where the leap in abstraction is particularly great (such as the Yoneda lemma), the reader will find careful and extensive explanations.