Re: A couple of simplicial questions

Todd Wilson asked on 3 Mar: The category Grp of groups has the property that every simplicial object in Grp satisfies the extension condition (i.e., is a so-called Kan complex). Is there a characterization of the categories with this property? Are there interesting uses of homotopy in these (other) categories? An answer may be found in A. Carboni, G.M. Kelly, and M.C. Pedicchio, Some remarks on Maltsev and Goursat categories, Applied Categorical Structures 1 (1993), 385-421. The slogan is "Kan = Maltsev". Max Kelly.