14 citations · 24 across the 11 of their papers we have counts for
4 papers · 1 filter
Idempotence for relative monads
Nathanael Arkor, Andrew Slattery
We study the concept of idempotence for relative monads, which exhibits several subtleties not present for non-relative monads. In particular, there is a bifurcation of notions of…
Magmal characterisations of cocartesian categories
Nathanael Arkor
We present a survey of characterisations of cocartesian categories in terms of monoidal categories - and, more generally, magmal categories - satisfying additional properties. In p…
Exponentiable virtual double categories and presheaves for double categories
Nathanael Arkor
Given a pair of pseudo double categories and , the lax functors from to , along with their transformations, modules, and multimodulati…
Bicategories of algebras for relative pseudomonads
Nathanael Arkor, Philip Saville, Andrew Slattery
We introduce pseudoalgebras for relative pseudomonads and develop their theory. For each relative pseudomonad , we construct a free--forgetful relative pseudoadjunction that exh…