Another definition of pointfree reloids

In previous post I stated that pointfree reloids can be defined as filters on pointfree funcoids.

Now I suggest also an alternative definition of pointfree reloids: Pointfree reloids can be defined as filters on products $latex \mathrm{atoms}\,\mathfrak{A} \times \mathrm{atoms}\,\mathfrak{B}$ of atoms of posets $latex \mathfrak{A}$ and $latex \mathfrak{B}$.

In the case if $latex \mathfrak{A}$ and $latex \mathfrak{B}$ are powerset lattices, this definition coincides with the definition of reloids (and with the definition of pointfree reloids given in the previous post).