The semibicategory of Moore automata
| Autor: | Boccali, Guido, Femić, Bojana, Laretto, Andrea, Loregian, Fosco, Luneia, Stefano |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study the semibicategory $\textsf{Mre}$ 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 $\textsf{Mly}$ 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 $\textsf{Mre}$ and $\textsf{Mly}$ is appreciated at the categorical level, as the equivalence induced between the fixpoints of an adjunction, in fact exhibiting $\textsf{Mre}(A,B)$ as a coreflective subcategory of $\textsf{Mly}(A,B)$; the comodality induced by this adjunction is but the $0$th step of a `level-like' filtration of the bicategory $\textsf{Mre}$ in a countable family of essential bi-localizations $\textsf{s}^n\textsf{Mre}\subseteq\textsf{Mre}$. We outline a way to generate intrinsically meaningful adjunctions of this form. We mechanize some of our main results using the proof assistant Agda. Comment: "The complexity of a bicategory of automata doubles every two months" (G.E.M., 1929--2023) |
| Databáze: | arXiv |
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