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Relation lifting, with an application to the many-valued cover modality

Marta Bilkova ; Alexander Kurz ; Daniela Petrisan ; Jiri Velebil.

We introduce basic notions and results about relation liftings on categories enriched in a commutative quantale. We derive two necessary and sufficient conditions for a 2-functor T to admit a functorial relation lifting: one is the existence of a distributive law of T over the "powerset monad" on&nbsp;[&hellip;]

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Extending set functors to generalised metric spaces

Adriana Balan ; Alexander Kurz ; Jiří Velebil.

For a commutative quantale $\mathcal{V}$, the category $\mathcal{V}-cat$ can be perceived as a category of generalised metric spaces and non-expanding maps. We show that any type constructor $T$ (formalised as an endofunctor on sets) can be extended in a canonical way to a type constructor&nbsp;[&hellip;]

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