Characterizing the commutator in varieties with a difference term

We extend the validity of Kiss’s characterization of “ [α ,β ]=0 ” from congruence modular varieties to varieties with a difference term. This fixes a recently discovered gap in our paper Kearnes et al. (Trans Am Math Soc 368:2115–2143, 2016). We also prove some related properties of Kiss terms in varieties with a difference term.