# “Funcoidal” reloids, a new research idea

Just today I’ve got the idea of the below conjecture:

Definition I call funcoidal such reloid $\nu$ that

$\mathcal{X} \times^{\mathsf{RLD}} \mathcal{Y} \not\asymp \nu \Rightarrow \\ \exists \mathcal{X}' \in \mathfrak{F}^{\mathrm{Base} ( \mathcal{X})} \setminus \{ 0 \}, \mathcal{Y}' \in \mathfrak{F}^{\mathrm{Base} ( \mathcal{Y})} \setminus \{ 0 \} : ( \mathcal{X}' \sqsubseteq \mathcal{X} \wedge \mathcal{Y}' \sqsubseteq \mathcal{Y} \wedge \mathcal{X}' \times^{\mathsf{RLD}} \mathcal{Y}' \sqsubseteq \nu)$
for every $\mathcal{X} \in \mathfrak{F}^{\mathrm{Src}\, \nu}$, $\mathcal{Y} \in \mathfrak{F}^{\mathrm{Dst}\, \nu}$.

Easy to prove proposition:

Proposition A reloid $\nu$ is funcoidal iff $x \times^{\mathsf{RLD}} y \not\asymp \nu \Rightarrow x \times^{\mathsf{RLD}} y \sqsubseteq \nu$ for every ultrafilters $x$ and $y$ on respective sets.

Conjecture $( \mathsf{RLD})_{\mathrm{in}}$ is a bijection from $\mathsf{FCD}( A ; B)$ to the set of funcoidal reloids from $A$ to $B$.