Applied Category Theory
Category theory reorganizes formal systems so that ideas from one field of mathematics translate into another, and this MIT OpenCourseWare course builds that framework through seven real-world applications rather than pure abstraction. Drawing on the approach of Fong and Spivak's Seven Sketches in Compositionality, the material covers topics such as databases, electrical circuits, and dynamical systems through the lens of categories, functors, and monoidal structures. Lecture notes, readings, and problem sets are provided so learners can work through the constructions themselves rather than just watch them explained. The course assumes some comfort with abstract mathematical reasoning but does not require prior exposure to category theory. As with other MIT OCW offerings, all materials are free to access and there is no certificate attached. It suits anyone who wants to see category theory used as a practical toolkit rather than treated purely as foundations for other pure mathematics.