14 citations · 36 across the 11 of their papers we have counts for
4 papers · 1 filter
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…
The nerve theorem for relative monads
Nathanael Arkor, Dylan McDermott
A fundamental result in the theory of monads is the characterisation of the category of algebras for a monad in terms of a pullback of the category of presheaves on the category of…
Relative monadicity
Nathanael Arkor, Dylan McDermott
We establish a relative monadicity theorem for relative monads with dense roots in a virtual equipment, specialising to a relative monadicity theorem for enriched relative monads.…
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…