I’ve found the following counter-example, to this conjecture: Example For a set $latex S$ of binary relations $latex \forall X_0,\dots,X_n\in S:\mathrm{up}(X_0\sqcap^{\mathsf{FCD}}\dots\sqcap^{\mathsf{FCD}} X_n)\subseteq S$ does not imply that there exists funcoid $latex f$ such that $latex S=\mathrm{up}\, f$. The proof is currently available…

read moreI start the “research-in-the middle” project (an outlaw offspring of Polymath Project) introducing to your attention the following conjecture: Conjecture The following are equivalent (for every lattice $latex \mathsf{FCD}$ of funcoids between some sets and a set $latex S$ of principal funcoids…

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