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math.CT2025
Ultracategories via Kan extensions of relative monads
Umberto Tarantino, Joshua Wrigley
Many structured categories of interest are most naturally described as algebras for a relative monad, but turn out nonetheless to be algebras for an ordinary monad. We show that, u…
math.CT2025
Day algebras
Edmund Robinson, Joshua Wrigley
In this paper we show that the Day monoidal product generalises in a straightforward way to other algebraic constructions and partial algebraic constructions on categories. This ge…