Pointfree topology regards certain order-theoretical structures, called frames, as topological spaces. We regard frames as spaces in virtue of the lattice of open set of every space being a frame. Not all frames are lattices of open sets; nonetheless, studying all frames as spaces offers...

We will investigate algebraic structures that are isomorphic to a set of partial functions equipped with selected operations (e.g. composition, intersection, etc.). I will spend most of the time describing results about completely representable algebras - these are the algebras that can be...

Following the study of the categorical features of preordered groups of [1], in this talk we study the category of right-preordered groups and monotone homomorphisms. We start by showing that this category has exactly the same exactness properties as the category of preordered groups....

The aim of this work is to explore the 1-dimensional algebraic Mal'tsev property from an Ord-enriched point of view. A 1-dimensional (regular) Mal'tsev category [2, 1] may be characterised through nice properties on (internal) relations such as:- every reflexive relation \( R \rightarrowtail...