Conjecture $\mathrm{dom}\, (\mathsf{RLD})_{\Gamma} f = \mathrm{dom}\, f$ and $\mathrm{im}\, (\mathsf{RLD})_{\Gamma} f = \mathrm{im}\, f$ for every funcoid $f$.
Conjecture $(\mathsf{RLD})_{\Gamma} g \circ (\mathsf{RLD})_{\Gamma} f = (\mathsf{RLD})_{\Gamma} (g \circ f)$ for every composable funcoids $f$ and $g$.
Conjecture For every funcoid $g$ we have $\mathrm{Cor}\, (\mathsf{RLD})_{\Gamma} g = (\mathsf{RLD})_{\Gamma} \mathrm{Cor}\, g$.