3 papers
math.CT2026
Presheaves and cocompletions in formal category theory
Nathanael Arkor, Dylan McDermott
We study the relationship between presheaf constructions and free cocompletions in the context of formal category theory, elucidating the coincidence between the two concepts in fa…
cs.PL2026
Denotational reasoning for asynchronous multiparty session types
Dylan McDermott, Nobuko Yoshida
We provide the first denotational semantics for asynchronous multiparty session types with precise asynchronous subtyping. Our semantics enables us to reason about asynchronous mes…
math.CT2025
The formal theory of relative monads
Nathanael Arkor, Dylan McDermott
We develop the theory of relative monads and relative adjunctions in a virtual equipment, extending the theory of monads and adjunctions in a 2-category. The theory of relative com…