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In the past I overlooked the following two open problems considering them obvious. When I tried to write proofs of these statements down I noticed these are not trivial. So I added them to my list of open problems.

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 $\mathcal{A}$.

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