Recently, Todd Wilson asked for a characterization of those categories wherein every simplicial object is Kan; and Michael Barr replied that this is so for a variety if and only if it admits a Maltsev operation, whereupon it suffices to imitate John Moore's original proof for the category of groups. Jack Duskin also recalls this unpublished observation of Michael's, remarking that he has his own proof. I noted that a complete proof has been published in [A.Carboni, G.M.Kelly, and M.C.Pedicchio, Some remarks on Maltsev and Goursat categories, Applied Categorical Structures 1(1993), 385-421]. I mention this again, since I failed to point out that our paper shows the equivalence Kan = Maltsev for any REGULAR category, where "Maltsev" now means that equivalence relations commute. The proof is pretty; it does follow the lines of John Moore's, but replaces his calculations with elements by reasonings about equivalence relations. Max Kelly.