Chapters: Ch 1 · Ch 2 · Ch 3 · Ch 4 · Ch 5
Category Theory
TheCatsters — Eugenia Cheng & Simon Willerton (YouTube) https://www.youtube.com/channel/UC5Y9H2KDRHZZTWZJtlH4VbA
Eugenia Cheng and Simon Willerton’s original category theory video lecture series recorded at the University of Sheffield — the first and still one of the best introductions to category theory on YouTube. Covers functors, natural transformations, adjunctions, limits, and monads in their natural mathematical habitat (rather than the Haskell-programmer’s perspective). [→ mathematics; category-theory]
Bartosz Milewski — Category Theory for Programmers (YouTube) https://www.youtube.com/channel/UC8BtBl8PNgd3vWKtm2yJ7aA
Author of Category Theory for Programmers (the Haskell-based textbook). His YouTube series presents category theory through the lens of Haskell types and functions — making abstract categorical concepts concrete through programming. The book/video series is the standard entry point for programmers approaching category theory. [→ mathematics; category-theory; scala-fp]
Edward Kmett (YouTube) https://www.youtube.com/channel/UCE3MJbkTVLoK8dAq7Del8ww
One of the most prolific Haskell library authors — lens, comonad, free, adjunctions, kan-extensions. His conference talks at Haskell Symposium and ICFP apply category theory directly to library design: adjunctions for monad transformers, comonads for spreadsheet evaluation, free monads for DSL construction. The deepest application of categorical thinking to practical programming. [→ mathematics; category-theory; scala-fp]
Topos Institute (YouTube & Web) https://topos.site/
The Topos Institute (Berkeley) applies category theory and applied category theory (ACT) to real-world problems in science, engineering, and social systems. Founded by John Baez, David Spivak, and others — produces research on categorical databases, epidemiological modeling, and the mathematical foundations of computation. Their UMAP explainer remains one of the most honest treatments of dimensionality reduction. [→ mathematics; category-theory; machine-learning-ai]
Algebra-Topology (YouTube — various) Research-level lecture series on algebraic topology, homological algebra, and their connections to category theory. Topics include simplicial sets, the nerve of a category, sheaf theory, and ∞-categories — the mathematical framework underlying much of modern theoretical computer science and physics. [→ mathematics; category-theory; topology]