6 papers · 1 filter
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 $\…
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…
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…
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 coalgebra…
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…