We need a more abstract way to define reloids:
For example filters on a set are isomorphic to triples where is a filter on , as well as filters of boolean reloids (that is pairs of functions , such that (for all and ).
I propose a way to encompass all ways to describe reloids as follows:
Let call a filtrator of pointfree reloid a pair of a filtrator and an associative operation on its core. Then call abstract reloids pointfree reloids isomorphic (both a filtrators and as semigroups) to reloids.
I am yet unsure that this structure encompasses all essential properties of reloids (just like as primary filtrators encompass all properties of filters on posets).