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math.CT2026
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
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
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…