§ Paredit via adjoints
- We posit that text editor movements ought to be endofunctions, and complementary keybinds ought to be adjoints to each other.
- With this in mind, what is the correct category for
paredit, and what are the adjunctions?
- Suppose we wish to build a theory of
Sexps. Then let's consider the category of rooted trees, where the root is the currently selected sexp, where the morphisms are inclusion maps of trees.
- What are the operations? They are going to be endofunctions in this category. For example, moving up to the parent, moving to the left and right sibling, etc.
- Hopf algebras and rooted trees (https://personal.math.ubc.ca/~thomas/TeXthings/HopfAlgebras-1.1.pdf)