outward reloid

Outward reloid of composition vs composition of outward reloids ★★

Author(s): Porton

\begin{conjecture} For every composable funcoids $f$ and $g$ $$(\mathsf{RLD})_{\mathrm{out}}(g\circ f)\sqsupseteq(\mathsf{RLD})_{\mathrm{out}}g\circ(\mathsf{RLD})_{\mathrm{out}}f.$$ \end{conjecture}

Keywords: outward reloid

Reloid corresponding to funcoid is between outward and inward reloid ★★

Author(s): Porton

\begin{conjecture} For any \href[funcoid]{http://www.wikinfo.org/index.php/Funcoid} $f$ and \href[reloid]{http://www.wikinfo.org/index.php/Reloid} $g$ having the same source and destination \[ ( \mathsf{\tmop{RLD}})_{\tmop{out}} f \subseteq g \subseteq ( \mathsf{\tmop{RLD}})_{\tmop{in}} f \Leftrightarrow ( \mathsf{\tmop{FCD}}) g = f. \] \end{conjecture}

Keywords: funcoid; inward reloid; outward reloid; reloid

Outward reloid corresponding to a funcoid corresponding to convex reloid ★★

Author(s): Porton

\begin{conjecture} $( \mathsf{\tmop{RLD}})_{\tmop{out}} ( \mathsf{\tmop{FCD}}) f = f$ for any \href[convex reloid]{http://www.wikinfo.org/index.php/Convex_reloid} $f$. \end{conjecture}

Keywords: convex reloid; funcoid; functor; outward reloid; reloid

Distributivity of outward reloid over composition of funcoids ★★

Author(s): Porton

\begin{conjecture} $( \mathsf{\tmop{RLD}})_{\tmop{out}} (g \circ f) = ( \mathsf{\tmop{RLD}})_{\tmop{out}} g \circ ( \mathsf{\tmop{RLD}})_{\tmop{out}} f$ for any composable \href[funcoids]{http://www.wikinfo.org/index.php/Funcoid} $f$ and $g$. \end{conjecture}

Keywords: distributive; distributivity; funcoid; functor; outward reloid; reloid

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