  We provide more characterizations of varieties having a term Mal'cev modulo
two functions $F$ and $G$. We characterize varieties neutral in the sense of
$F$, that is varieties satisfying $R \subseteq F(R)$. We present examples of
global operators satisfying the homomorphism property, in particular we show
that many known commutators satisfy the homomorphism property.

Rings and Algebras