Categories for the working programmers Live-Code Notebooks exploring monoidal programming languages Monads Monad categories and algebras defined by actual group theoretic examples of Action groups and η, μ Natural Transformations naturally defined and finally programmed. Transformations η , μ Simplex Category Δ Δ is a category defined with finite ordered integers set as objects and non-decreasing maps as morphisms. ΔSys: String and Term Rewriting for Simplex Category