Earlier I have conjectured that the set of funcoids is order-isomorphic to the set of filters on the set of finite joins of funcoidal products of two principal filters. For an equivalent open problem I found a counterexample.
Now I propose another similar but weaker open problem:
Conjecture Let be a set. The set of funcoids on is order-isomorphic to the set of filters on the set (moreover the isomorphism is (possibly infinite) meet of the filter), where is the set of unions where is a finite partition of and for every
The last conjecture is equivalent to this question formulated in elementary terms. If you solve this (elementary) problem, it could be a major advance in mathematics.