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math.CT2025
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…
math.CT2025
Hofmann-Streicher lifting of fibred categories
Andrew Slattery, Jonathan Sterling
In 1997, Hofmann and Streicher introduced an explicit construction to lift a Grothendieck universe from the category of sets into the category of set-valued presheaves on a small c…
math.CT2025
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…