Graduation Year


Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science



Reader 1

Vin de Silva

Reader 2

Dagan Karp

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2020 Luke Trujillo


Mac Lane’s Coherence Theorem is a subtle, foundational characterization of monoidal categories, a categorical concept which is now an important and popular tool in areas of pure mathematics and theoretical physics. Mac Lane’s original proof, while extremely clever, is written somewhat confusingly. Many years later, there still does not exist a fully complete and clearly written version of Mac Lane’s proof anywhere, which is unfortunate as Mac Lane’s proof provides very deep insight into the nature of monoidal categories. In this thesis, we provide brief introductions to category theory and monoidal categories, and we offer a precise, clear development of Mac Lane’s ideas towards a complete proof of the coherence theorem. This thesis will hopefully provide future readers a thorough introduction to monoidal categories and a clearly written proof of Mac Lane’s Coherence Theorem, saving those who are interested in truly understanding Mac Lane’s theorem dozens of hours of their time.