The main goal of this talk is to extend results from point-free topology to more general settings. We start by studying how the notions of sublocale and localic map can be extended from locales (i.e. complete Heyting algebras) to Heyting semilattices. Motivated by the case of Heyting...

Graduated categories were introduced in [1] in order to prove that finitary endofunctors are right adjoints iff they preserve countable limits. Recently, these categories turned out to be useful in categorical colagebra: every finitary endofunctor preserving finite intersections has a...