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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 11th 2009

    Fixed the comments in the reference list at model structure on dg-algebras: Gelfand-Manin just discuss the commutative case. The noncommutative case seems to be due to the Jardine reference. Or does anyone know an earlier one?

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 11th 2009

    I have a question at model structure on dg-algebras on the invariant characterization of commutative dg-algebras within all dg-algebras.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 11th 2009

    I added an "Idea" section to model structure on dg-algebras

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 11th 2009
    • (edited Nov 11th 2009)

    I added a theorem from the book by Igor Kriz and Peter May about how commutative dg-algebras already exhaust, up to weak equivalence, all homotopy-cmmutative dg-algebras to model structure on dg-algebras.

    (this might better fit into some other entry eventually, though)

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 11th 2009

    Added the statement that the forgetful functor from commutative dg-algebras to all dg-algebras is the right adjoint part of a Quillen adjunction with respect to the given modelstructures.

    • CommentRowNumber6.
    • CommentAuthorzskoda
    • CommentTimeNov 11th 2009
    I would look into Hinich's 1995 or so paper, for a possible earlier reference.
    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeNov 12th 2009
    • (edited Nov 12th 2009)

    created a section on cofibrations in CdgAlg and hence on Sullivan algebras.

    Created entry for Dennis Sullivan in that context. Always nice to create an entry and see that the "timeline"-entry was already requesting it.

    I suppose I'll have the following sorted out in a minute, but maybe somebody is quicker with helping me:

    in the definition of a relative Suillvan algebra  (A,d) \hookrightarrow (A \otimes \wedge V, d') I suppose we do require that  d' restricted to  A acts like  d plus a term that contains elements in V ?

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeNov 29th 2010

    I started at model structure on dg-algebras a new subsection on Unbounded dg-algebras, stating a basic existence result.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeDec 9th 2010

    added a section Simplicial hom-objects to model structure on dg-algebras on the derived hom-spaces for unbounded commutative dg-algebras (over a field of char 0).

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeDec 9th 2010
    • (edited Dec 9th 2010)

    okay, I think I finally have assembled the full proof that the derived copowering of undbounded commutative dg-algebras (over field of char 0) over degreewise finite simplicial sets is given by the polynomial-differential-forms-on-simplices-functors. I have written this out now at Derived powering over sSet.

    This provides the missing detail for the discussion that 𝒪(S1)kk[1] over at Hochschild cohomology. This is supposed to be all very obvious, but it took me a bit to assemble all the details properly, anyway.

    I now moved other discussion of the model structure on commutative unbounded dg-algebras from the Hochschild entry over to model structure on dg-algebras. This mainly constituting the other new section Derived co-powering over sSet.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeDec 10th 2010

    I added statement and proof that ([n]Hom(A,BΩpoly(Δ[n]))) is a Kan complex when A is cofibrant.

    Also added an earlier reference by Ginot et al where it is discussed that their “derived copowering” of cdgAlg over sSet indeed lands in commutative dg-algebras. I’ll try to add more technical details on how this works later on.

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeJul 16th 2014
    • (edited Jul 16th 2014)

    there was an old question of how (to which extent) the homotopy theory of commutative dg-algebras is homotopy-faithful inside that of all dg-algebras.

    Recently there appeared some discussion of this issue in

    I have added pointers to this here.

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeFeb 21st 2017
    • (edited Feb 21st 2017)

    I have added to the section on the Bousfield-Gugenheim model structure a subsection on its simplicial hom-complexes which almost but not quite, make for a simplicial model category structure.

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeAug 19th 2020

    trying to bring some order into the list of references, adding some subsections…

    diff, v63, current

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeAug 19th 2020

    have equipped more of the Definitions/Propositions with pointers to page-and-verse in Bousfield-Gugenheim and in Gelfand-Manin.

    diff, v63, current

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeAug 21st 2020
    • (edited Aug 21st 2020)

    Added full publication data to:

    Around Example 3.7, these authors make (somewhat implicitly) the observation that the Bousfield-Gugenheim model structure on connective rational dgc-algebras (which B&G and later Gelfand&Manin establish by laborious checks) is simply that right transferred from the projective model structure on chain complexes – which makes the proof that relative Sullivan models are cofibrations a triviality.

    So this is all very nice, and highlighted as such in Hess’s recview. But neither of these authors states this as a theorem that could be properly cited as such, instead they leave it at side remarks. Is there any author who has published this in more citeable form?

    diff, v67, current

    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeAug 23rd 2020
    • CommentRowNumber18.
    • CommentAuthorUrs
    • CommentTimeSep 1st 2020

    added statement (here) that quasi-isos are preserved by pushout along relative Sullivan algebras

    diff, v71, current

    • CommentRowNumber19.
    • CommentAuthorUrs
    • CommentTimeJul 7th 2021

    I have added (here) statement and proof of the change-of-scalars Quillen adjunction

    (dgcAlg0k)proj()Qures(dgcAlg0)proj

    diff, v75, current

    • CommentRowNumber20.
    • CommentAuthorTodd_Trimble
    • CommentTimeJul 11th 2021

    Changed to k.

    • CommentRowNumber21.
    • CommentAuthorUrs
    • CommentTimeJul 11th 2021

    Ah, right. Thanks.