41 citations · 136 across the 32 of their papers we have counts for
33 papers
Two-dimensional transducers
Fosco Loregian
We define a bicategory whose 1-cells provide a categorification of transducers, computational devices extending finite-state automata with output capabilities. This…
Doctrinal Semantics of Directed First-Order Logic
Andrea Laretto, Fosco Loregian, Niccolò Veltri
We present a first-order logic equipped with an "asymmetric" directed notion of equality, which can be thought of as rewrites between terms, allowing for types to be interpreted as…
Monads and limits in bicategories of circuits
Fosco Loregian
We study monads in the (pseudo-)double category where loose arrows are Mealy automata valued in an ambient monoidal category , and the cate…
Di- is for Directed: First-Order Directed Type Theory via Dinaturality
Andrea Laretto, Fosco Loregian, Niccolò Veltri
We show how dinaturality plays a central role in the interpretation of directed type theory where types are interpreted as (1-)categories and directed equality is represented by $\…
Fibrations of algebras
Danel Ahman, Greta Coraglia, Davide Castelnovo +3
We study fibrations arising from indexed categories of the following form: fix two categories and a functor $F : \mathcal{A} \times \mathcal{X} \longright…
Automata and coalgebras in categories of species
Fosco Loregian
We study generalized automata (in the sense of Adámek-Trnková) in Joyal's category of (set-valued) combinatorial species, and as an important preliminary step, we study coalgebras…
Adjoint functor theorems for lax-idempotent pseudomonads
Nathanael Arkor, Ivan Di Liberti, Fosco Loregian
For each pair of lax-idempotent pseudomonads and , for which is locally fully faithful and distributes over , we establish an adjoint functor theorem, relating $R…
The semibicategory of Moore automata
Guido Boccali, Bojana Femić, Andrea Laretto +2
We study the semibicategory of "Moore automata": an arrangement of objects, 1- and 2-cells which is inherently and irredeemably nonunital in dimension one. Between t…
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 -automata, where the span of maps that usually defines a determinist…
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…
Fibrational Linguistics (FibLang): Language Acquisition
Fabrizio Genovese, Fosco Loregian, Caterina Puca
In this work we show how FibLang, a category-theoretic framework concerned with the interplay between language and meaning, can be used to describe vocabulary acquisition, that is…
Fibrational linguistics: First concepts
Fabrizio Genovese, Fosco Loregian, Caterina Puca
We define a general mathematical framework for linguistics based on the theory of fibrations, called FibLang. We start by modelling the interaction between linguistics and cognitio…
Escrows are optics
Fabrizio Genovese, Fosco Loregian, Daniele Palombi
We provide a categorical interpretation for escrows, i.e. trading protocols in trustless environment, where the exchange between two agents is mediated by a third party where the b…
Differential 2-rigs
Fosco Loregian, Todd Trimble
We study the notion of a "differential 2-rig", a category R with coproducts and a monoidal structure distributing over them, also equipped with an endofunctor D : R -> R that satis…
A Categorical Semantics for Bounded Petri Nets
Fabrizio Romano Genovese, Fosco Loregian, Daniele Palombi
We provide a categorical semantics for bounded Petri nets, both in the collective- and individual-token philosophy. In both cases, we describe the process of bounding a net interna…
Nets with Mana: A Framework for Chemical Reaction Modelling
Fabrizio Romano Genovese, Fosco Loregian, Daniele Palombi
We use categorical methods to define a new flavor of Petri nets where transitions can only fire a limited number of times, specified by a quantity that we call mana. We do so with…
Rosen's no-go theorem for regular categories
Fosco Loregian
The famous biologist Robert Rosen argued for an intrinsic difference between biological and artificial life, supporting the claim that `living systems are not mechanisms'. This res…
Coends of higher arity
Fosco Loregian, Emily de Oliveira Santos
We specialise a recently introduced notion of generalised dinaturality for functors to the case where the domai…
Functorial Semantics for Partial Theories
Ivan Di Liberti, Fosco Loregian, Chad Nester +1
We provide a Lawvere-style definition for partial theories, extending the classical notion of equational theory by allowing partially defined operations. As in the classical case,…
t-structures on stable infinity-categories
Fosco Loregian
The present work re-enacts the classical theory of t-structures reducing the classical definition given in *Faisceaux Pervers* to a rather primitive categorical gadget: suitable re…
Profunctor Optics, a Categorical Update
Bryce Clarke, Derek Elkins, Jeremy Gibbons +4
Optics are bidirectional data accessors that capture data transformation patterns such as accessing subfields or iterating over containers. Profunctor optics are a particular choic…
A Fubini rule for -coends
Fosco Loregian
We prove a Fubini rule for -co/ends of -functors . This allows to lay down "integration rules", similar to t…
A standard theorem on adjunctions in two variables
Fosco Loregian
We record an explicit proof of the theorem that lifts a two-variable adjunction to the arrow categories of its domains.
On the unicity of formal category theories
Ivan Di Liberti, Fosco Loregian
We prove an equivalence between cocomplete Yoneda structures and certain proarrow equipments on a 2-category . In order to do this, we recognize the presheaf constructi…