linguistic:voice_change, structural:reformatting, stylistic:style_transfer
Lattices

The equivalence relations on any set X, when ordered by set inclusion, form a complete lattice, called Con X by convention. The canonical map ker : X ^ X → Con X, relates the monoid X ^ X of all functions on X and Con X. ker is surjective but not injective. Less formally, the equivalence relation ker on X, takes each function f : X → X to its kernel ker f. Likewise, ker(ker) is an equivalence relation on X ^ X.