§ 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)