Categories for the Working Mathematician

This book offers foundational insights into category theory, covering key concepts like functors, natural transformations, and adjoint functors. It includes recent advancements and applications, particularly in monoidal and higher-dimensional categories.

Categories for the Working Mathematician is a comprehensive resource that explores fundamental concepts in category theory, making it applicable across various fields. The book begins with foundational ideas, including categories, functors, natural transformations, and duality. These concepts serve as the building blocks for more complex topics, such as symmetric monoidal categories, braided monoidal categories, and their associated coherence theorems.

As the book progresses, it delves into the topic of adjoint functors, which are essential for understanding universal constructions. The author provides a thorough analysis of how functors can be represented by sets of morphisms and discusses techniques for manipulating direct and inverse limits. Throughout the chapters, these categorical concepts are illustrated with numerous applications, particularly focusing on the basic existence theorem for adjoint functors. The construction of categories based on algebraic systems is also examined, with insights drawn from Beck's theorem.

The second edition of this influential text includes significant revisions and new content, featuring two additional chapters that address contemporary topics of interest. One chapter focuses on symmetric and braided monoidal categories, while the other explores 2-categories and higher-dimensional categories, which have gained traction in recent mathematical discourse. The bibliography has been expanded to encompass recent advancements in the field, making this edition a valuable resource for both established mathematicians and those new to category theory.