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 dis
tributive law of T over the powerset monad on categories, one is the preservation by T of exactness of certain squares. Both characterisations are generalisations of the classical results known for set functors: the first characterisation generalises the existence of a distributive law over the genuine powerset monad, the second generalises preservation of weak pullbacks. The results presented in this paper enable us to compute predicate liftings of endofunctors of, for example, generalised (ultra)metric spaces. We illustrate this by studying the coalgebraic cover modality in this setting.
We analyse the all-sky Leiden/Argentina/Bonn HI survey, where we identify shells belonging to the Milky Way. We used an identification method based on the search of continuous regions of a low brightness temperature that are compatible with given pro
perties of HI shells. We found 333 shells in the whole Galaxy. The size distribution of shells in the outer Galaxy is fitted by a power law with the coefficient of 2.6 corresponding to the index 1.8 in the distribution of energy sources. Their surface density decreases exponentially with a scale length of 2.8 kpc. The surface density of shells with radii >= 100 pc in the solar neighbourhood is around 4 per kpc^2 and the 2D porosity is approximately 0.7.
