Yes, it is in my paper with Kelly and Pedicchio 'Some Remarks on Maltsev and Goursat Categories', (Applied Mathematical Structures 1, 385-421, 1993) where it is proved more generally for regular categories (Theorem 4.2, p. 404). Aurelio Carboni At 16.28 13/09/2011, you wrote:

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

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