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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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Moss' logic for ordered coalgebras

Marta Bílková ; Matěj Dostál.

We present a finitary version of Moss' coalgebraic logic for $T$-coalgebras, where $T$ is a locally monotone endofunctor of the category of posets and monotone maps. The logic uses a single cover modality whose arity is given by the least finitary subfunctor of the dual of the coalgebra functor&nbsp;[&hellip;]

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