Papers › The semibicategory of Moore automata
The semibicategory of Moore automata
Guido Boccali, Bojana Femić, Andrea Laretto, Fosco Loregian, Stefano Luneia
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We study the semibicategory Mre of "Moore automata": an arrangement of objects, 1- and 2-cells which is inherently and irredeemably nonunital in dimension one. Between the semibicategory of Moore automata and the better behaved bicategory Mly of "Mealy automata" a plethora of adjunctions insist: the well-known essential equivalence between the two kinds of state machines that model the definitions of Mre and Mly is appreciated at the categorical level, as the equivalence induced between the fixpoints of an adjunction, in fact exhibiting Mre(A,B) as a coreflective subcategory of Mly(A,B); the comodality induced by this adjunction is but the 0th step of a `level-like' filtration of the bicategory Mre in a countable family of essential bi-localizations sⁿMre⊆Mre. We outline a way to generate intrinsically meaningful adjunctions of this form. We mechanize some of our main results using the proof assistant Agda.
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