outward reloid


Outward reloid of composition vs composition of outward reloids ★★

Author(s): Porton

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

Keywords: outward reloid

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

Author(s): Porton

Conjecture   For any funcoid $ f $ and reloid $ g $ having the same source and destination \[ ( \mathsf{\tmop{RLD}})_{\tmop{out}} f \subseteq g \subseteq (    \mathsf{\tmop{RLD}})_{\tmop{in}} f \Leftrightarrow ( \mathsf{\tmop{FCD}}) g    = f. \]

Keywords: funcoid; inward reloid; outward reloid; reloid

Distributivity of outward reloid over composition of funcoids ★★

Author(s): Porton

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 funcoids $ f $ and $ g $.

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

Syndicate content