Another question about Kan

Is the following known? An equational category has the property that every simplicial object is Kan iff it is a Mal'cev category. This means that there is a ternary operation I call <-,-,-> such that <x,y,y> = x and <x,x,y> = y. In a sense this is not surprising. The Kan condition makes homotopy an equivalence relation. The degeneracies make homotopy reflexive and Mal'cev categories are characterized by the fact that every reflexive binary relation is an equivalence relation. Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]