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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeFeb 24th 2011
    • (edited Feb 24th 2011)

    I think I can see the following, but am wondering if this is discussed in the literature:

    for AA a cochain dg-algebra in non-negative degree let ΞAAlg Δ\Xi A \in Alg^\Delta be the cosimplicial algebra obtained as its image under dual Dold-Kan. Then regarded as an object in [Δ op,Alg op][Δ op,(Alg Δ) op][\Delta^{op}, Alg^{op}] \hookrightarrow [\Delta^{op}, (Alg^\Delta)^{op}] it should always be Reedy cofibrant, for the projective model structure on Alg ΔAlg^\Delta where the fibrations are degreewise surjections:

    because the morphism out of the latching object in degree nn is dually a projection out of the algebra (ΞA) n(\Xi A)_n discarding some top degree generators, hence is an epi, hence a fibration in Alg proj ΔAlg^\Delta_{proj} hence a cofibration (Alg proj Δ) op(Alg^\Delta_{proj})^{op}.

    This statement should be of general relevance and is probably discussed somewhere. Does anyone have anything?