John Baez publishes free Applied Category Theory course with full lecture notes and videos
UC Riverside mathematician John Baez has published complete materials for his Applied Category Theory course online, including lecture notes, exercises with solutions, and video recordings covering categorical approaches to networks, databases, and dynamical systems.
John Baez, a mathematical physicist at UC Riverside, has published full course materials for Applied Category Theory as a free online resource. The site includes lecture notes, problem sets with solutions, and video recordings spanning functors and natural transformations, adjoint functors, monoidal categories, and enriched categories — with applications to Petri nets, electrical circuits, and chemical reaction networks.
The course targets graduate students and practitioners seeking working knowledge of category theory beyond pure abstraction. Exercises draw from real-world modeling problems in biology, engineering, and computer science. Video lectures walk through the same examples covered in written notes, and problem sets include detailed solutions designed to build intuition for how categorical constructions map onto concrete computational structures.
For the open-source AI community, category theory has become a formal framework for reasoning about composable architectures. Functorial approaches to neural network design, monoidal categories for tensor operations, and categorical semantics for probabilistic programming all draw on the toolkit Baez's course covers. Practitioners building modular AI systems — especially those working on compositional generalization, equivariant networks, or differentiable programming — increasingly encounter categorical abstractions in research papers and library documentation. Baez co-authored Seven Sketches in Compositionality with Brendan Fong, a standard reference in the field.
