- Could one re-invent the whole curriculum from age 5 onwards
built on new [category theoretic] concepts?
If I were starting from scratch, and I’m always starting from scratch, I would ease my way up to the pons asinorum of logic and math using the types of logical graphs laid down by Peirce and Spencer Brown. That is because I think it’s crucial to firm up propositional logic before taking on quantifiers and to grasp classical logic before intuitionistic.
The climb from “zeroth order logic” to first order logic is a lot more interesting and richer in adventure once you have a truly efficient calculus for propositional logic at the ready. An approach to categories, combinators, etc. can then be made via the propositions as types analogy. For the kiddies, Smullyan’s Mockingbird would be the primer of choice.