Videos
The videos on my YouTube channel, Maps of Math, run loosely in parallel with the writing — usually well ahead of it. I use the channel as a place to work through ideas before they go into the book, which means the videos don’t track the book’s chapter order. I hop around topics as I think through them. Below they are grouped by topic; within each group, ordered by when they were recorded.
Course orientation
- What This Course Is About — Mar 17, 2026
- Basics of Functions — Mar 19, 2026
Set theory
- Basics of Set Theory — Mar 18, 2026
Category theory
Foundations
- What are categories? — Mar 23, 2026
- Opposite Categories aren’t cute tricks! — Apr 8, 2026
- What is Mathematical Structure? — Apr 17, 2026
Functors
- What are functors? — Mar 24, 2026
- Covariant and Contravariant Functors — Apr 8, 2026
- Profunctors & Heteromorphisms — Apr 12, 2026
Natural transformations
- What are natural transformations? — Apr 4, 2026
- What is a natural isomorphism? — Apr 9, 2026
- What are functor categories? — May 6, 2026
Representability and Yoneda
- Representable Functors — Apr 10, 2026
- Representable Profunctors — Apr 14, 2026
- What is the Category of Elements? — May 12, 2026
- Why Representable Functors Matter — May 14, 2026
- Why Representable Functors Matter 2 — Gory Details — May 16, 2026
Universal constructions
- Initial & Terminal Objects — Apr 20, 2026
- Points of Existence & Co-Points of Nullity — Apr 21, 2026
- What are Mono(morphism)s & Epi(morphism)s? — Apr 23, 2026
- How zero objects enable abstract algebra — Apr 24, 2026
Limits and colimits
- What are Limits & Colimits? — May 7, 2026
Comma and slice categories
- Comma Categories — The most important categorical structure — May 2, 2026
- What are slice & coslice categories? — May 3, 2026
Adjunctions
- What Are Adjoint Functors? — Apr 15, 2026
Abstract algebra
- What is a Group? — Apr 28, 2026
- What is a Ring? — Apr 28, 2026
- Commutative / Function-like Rings vs Non-Commutative / Operator-like Rings — Apr 28, 2026
Multilinear and geometric algebra
- What is the tensor algebra? — Mar 20, 2026