We will discuss a non-pointed version of the notion of torsion theory, in the framework of categories equipped with a posetal monocoreflective subcategory such that the coreflector inverts monomorphisms. We will explore the relationships of such torsion theories with factorization systems...

Codensity monads provide a universal method to generate complex monads from simple functors. Recently, important monads in logic, denotational semantics, and probabilistic computation (such as ultrafilter monads, the Vietoris monad, and the Giry monad) have been presented as codensity...