# Is CosimplicialAlgebras left proper?

The model category structure on co-simplicial commutative $k$-algebras, $CAlg_k^\Delta$, with fibrations degreewise surjections: is it left proper?

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Hi Urs, this may or may not be useful to you, but there is a proof of properness for a certain model structure on commutative monoids in symmetric spectra. See Hornbostel (arXiv:1005.4546, Thm 3.17), and the reference he gives to Shipley: A convenient model structure... (article available on her webpage). Maybe some idea used in this proof could also be useful in your setting. –  Andreas Holmstrom Aug 26 '10 at 22:04
Thanks, Andreas. Not sure yet if that helps, but I'll see. Maybe I should mention that I am quite aware of a few statements that are awefully close to the one I am after. For instance I know that simplicial commutative algebras are left proper. And for simplicial algebras in a very general sense there is this powerful article by Charles Rezk "Every homotopy theory of simplicial algebras admits a proper model" (arxiv.org/abs/math/0003065) . Maybe I am being dense and this implies the statement for cosimplicial algebras trivially, but I am not sure. –  Urs Schreiber Aug 27 '10 at 9:11