Question $(\mathsf{RLD})_{\mathrm{out}} ( \mathcal{A} \times^{\mathsf{FCD}} \mathcal{B}) = \mathcal{A} \times^{\mathsf{RLD}} \mathcal{B}$ for every filter objects $\mathcal{A}$, $\mathcal{B}$?
Conjecture $(\mathsf{RLD})_{\mathrm{out}} {(=)}|_{\mathcal{A}} = {(=)}|_{\mathcal{A}}$ for every filter object $\mathcal{A}$.