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).
We can identify one-element relations as atoms of our poset. It remains to prove that our structure determines binary relations up to re-order (bijections) of variables
and
.
Correction: It is not a semigroup, it is a precategory.