Stefano Luneia

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math.CT2025

The Morita $(\infty, 2)$ -category of a monoidal category as a $2$ -complicial set

Arghan Dutta, Stefano Luneia, Martina Rovelli +1

We provide an explicit and elementary construction of the Morita $(\infty, 2)$ -category of a monoidal category which satisfies minimal conditions. We construct it as a $3$ -coskeleta…

math.CT2023

The semibicategory of Moore automata

Guido Boccali, Bojana Femić, Andrea Laretto +2

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 t…

math.CT2023

Completeness for categories of generalized automata

Guido Boccali, Andrea Laretto, Fosco Loregian +1

We present a slick proof of completeness and cocompleteness for categories of $F$ -automata, where the span of maps $E \leftarrow E \otimes I \to O$ that usually defines a determinist…

math.CT2023

Bicategories of Automata, Automata in Bicategories

Guido Boccali, Andrea Laretto, Fosco Loregian +1

We study bicategories of (deterministic) automata, drawing from prior work of Katis-Sabadini-Walters, and Di Lavore-Gianola-Román-Sabadini-Sobociński, and linking their bicategorie…

The Morita (∞,2)-category of a monoidal category as a 2-complicial set

The semibicategory of Moore automata

Completeness for categories of generalized automata

Bicategories of Automata, Automata in Bicategories

The Morita $(\infty, 2)$ -category of a monoidal category as a $2$ -complicial set