45 citations · 96 across the 11 of their papers we have counts for
11 papers
Extending set functors to generalised metric spaces
Adriana Balan, Alexander Kurz, Jiří Velebil
For a commutative quantale , the category can be perceived as a category of generalised metric spaces and non-expanding maps. We show that any type c…
An elementary characterisation of sifted weights
Matěj Dostál, Jiří Velebil
Sifted colimits (those that commute with finite products in sets) play a major role in categorical universal algebra. For example, varieties of (many-sorted) algebras are precisely…
Positive fragments of coalgebraic logics
Adriana Balan, Alexander Kurz, Jiří Velebil
Positive modal logic was introduced in an influential 1995 paper of Dunn as the positive fragment of standard modal logic. His completeness result consists of an axiomatization tha…
Kan injectivity in order-enriched categories
Jiri Adamek, Lurdes Sousa, Jiri Velebil
Continuous lattices were characterised by Martin Escardo as precisely the objects that are Kan-injective w.r.t. a certain class of morphisms. We study Kan-injectivity in general ca…
Relation lifting, with an application to the many-valued cover modality
Marta Bilkova, Alexander Kurz, Daniela Petrisan +1
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…
Relation Liftings on Preorders and Posets
Marta Bilkova, Alexander Kurz, Daniela Petrisan +1
The category Rel(Set) of sets and relations can be described as a category of spans and as the Kleisli category for the powerset monad. A set-functor can be lifted to a functor on…