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math.CT2024
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 $\…
math.CT2024
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…
math.CT2024
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…