Subject: Chain complexes and simplicial model categories From: Llorenç Rubió Date: Tue, 23 May 2006 11:51:23 +0200 Dear all, It seems to be folklore that the category Ch(R) of chain complexes of R-modules is not a simplicial model category. That is said for example after definition 4.2.18 in Hovey's Model Categories. 1. What the tensor product X\otimes K of a chain complex X and a simplicial set K should be? 2. And the cotensor X^K? 3. The reason of not being a simplicial model category is in SM7 or elsewhere? Finally, in Jardine's paper Presheaves of Chain Complexes is stated (lemma 2.5) that the category Ch_+(R) of positively graded chain complexes of R-modules has the structure of a monoidal proper closed simplicial model category, via the Dold-Kan correspondence, but the chain complex tensor product is not the standard. Again there is not specified the tensor and cotensor by a simplicial set. Llorenç Rubió