Tangling in dualisability of unary algebras

We look at non-dualisable {0, 1}-valued finite unary algebras with 0 where meet is defined on the algebra and join is partially defined. More specifically, we look at Join Upper Bounded Algebras with unique rows, as well as two types of Join Upper Bounded Algebras with non-unique rows: non-one-double-algebras and one-doubled-algebras. We then determine what tangled functions need to be included for an extension of the algebra to be dualisable. It turns out that just including the tangled functions for non-one-doubled-algebras and one-doubled-algebras is not enough to guarantee dualisability. We then define the additional functions needed for dualisability of the extension. --Leaf i.