YonedaLab
An interactive category theory playground where math and CS grad students define categories in a typed DSL and the app auto-computes Yoneda embeddings, hom-sets, natural transformations, and renders them as explorable commutative diagrams — each concept accompanied by a tangible everyday analogy.
Math and CS graduate students, Haskell programmers, and theoretical CS researchers learning or teaching category theory
- Typed DSL for defining categories (objects, morphisms, composition laws) with auto-rendered commutative diagrams
- One-click "Compute Yoneda embedding" with a side-panel narrative that explains what each lemma is doing in plain language
- Built-in analogy library (Alice-and-Bob-style scenes, ropes-and-pulleys, etc.) attached to each concept, plus instructor mode for slide generation
- Export diagrams to LaTeX/TikZ and runnable Haskell snippets for theses, blog posts, or coursework assignments
Milewski-style analogies-first pedagogy resonates with programmer-mathematicians, and existing category-theory tooling (Sage, Mathematica) is heavy and assumes the abstractions are already known — a lightweight browser playground lowers the entry ramp.
Category theory has a stable but small dedicated community: Milewski's free book, MIT Learn course, Applied Category Theory school, and CoRecursive podcast — but audience is confined to grad students and Haskell programmers, not mainstream.Category Theory - CoRecursive Podcast (Bartosz Milewski) ↗Category Theory for Scientists | MIT Learn ↗
Multiple interactive category theory tools already exist: MathAtlas (drag-and-drop diagrams, Yoneda coverage), Vectree visual explainer, and the open-source rsthornton/category-theory-trainer on GitHub — so the claimed 'no existing playground' framing is inaccurate.Category Theory (Visual Intro) | MathAtlas ↗GitHub - rsthornton/category-theory-trainer ↗category theory — Visual Explainer | Vectree ↗
Niche grad-student/Haskell audience with strong free alternatives (Milewski PDF is CC-licensed, MIT course is free, nLab free, CatLab open-source) — no evidence of willingness to pay for a category-theory playground specifically.PDF Category Theory for Programmers (free, CC BY-SA) ↗Category Theory for Scientists | MIT Learn ↗
Category theory is a mature academic field with stable interest over decades; applied CT and Haskell ecosystem keep pedagogy demand steady but the audience is unlikely to surge.Resources - APPLIED CATEGORY THEORY ↗
Building a typed DSL plus Yoneda/hom-set/natural-transformation computation plus commutative-diagram rendering plus analogies is non-trivial engineering; existing tools (MathAtlas, Catlab.jl) had to be built by people with deep domain expertise.Categorical Algebra for R • catlab ↗Category Theory (Visual Intro) | MathAtlas ↗