Conjecture $latex \mathrm{dom}\, (\mathsf{RLD})_{\Gamma} f = \mathrm{dom}\, f$ and $latex \mathrm{im}\, (\mathsf{RLD})_{\Gamma} f = \mathrm{im}\, f$ for every funcoid $latex f$.
Conjecture $latex (\mathsf{RLD})_{\Gamma} g \circ (\mathsf{RLD})_{\Gamma} f = (\mathsf{RLD})_{\Gamma} (g \circ f)$ for every composable funcoids $latex f$ and $latex g$.
Conjecture For every funcoid $latex g$ we have $latex \mathrm{Cor}\, (\mathsf{RLD})_{\Gamma} g = (\mathsf{RLD})_{\Gamma} \mathrm{Cor}\, g$.
See my research monograph and related articles for the definitions.