Abstract
Starting with the notion of a deterministic automaton, we formalize and explore the concepts of macros, operator overloading and refinement. The category of automata whose arrows are refinements is defined and two closure operators (idempotent monads) on this category are given. The first monad arises as an adjunction with the category of concrete monoids and corresponds to closure by macros, while the other monad comes from an adjunction with the category of graphs and corresponds to closure by overloading.This theory explicates a connection (also called the Catalan construction) between monoids and graphs. Directions for further research are suggested.
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