Ah, right. Thanks.

]]>Changed $\mathbb{R}$ to $k$.

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

$\big( dgcAlg^{\geq 0}_k \big)_{proj} \underoverset {\underset{res_{\mathbb{Q}}}{\longrightarrow}} {\overset{ (-) \otimes_{\mathbb{Q}} \mathbb{R} }{\longleftarrow}} {\bot_{\mathrlap{Qu}}} \big( dgcAlg^{\geq 0}_{\mathbb{Q}} \big)_{proj}$ ]]>added statement (here) that quasi-isos are preserved by pushout along relative Sullivan algebras

]]>added paragraph on the Quillen adjunction between simplicial sets and connective dgc-algebras

]]>Added full publication data to:

- Paul Goerss, Kirsten Schemmerhorn,
*Model categories and simplicial methods*, Notes from lectures given at the University of Chicago, August 2004, in:*Interactions between Homotopy Theory and Algebra*, Contemporary Mathematics 436, AMS 2007(arXiv:math.AT/0609537, doi:10.1090/conm/436)

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?

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

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

]]>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.

]]>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

Ilias Amrani,

*Comparing commutative and associative unbounded differential graded algebras over Q from homotopical point of view*(arXiv:1401.7285)Ilias Amrani,

*Rational homotopy theory of function spaces and Hochschild cohomology*(arXiv:1406.6269)

I have added pointers to this here.

]]>I added statement and proof that $([n] \mapsto Hom(A, B \otimes \Omega^\bullet_{poly}(\Delta[n])))$ 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.

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 $\mathcal{O}(S^1) \simeq k \oplus k[-1]$ 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.

]]>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).

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

]]>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 I suppose we do require that restricted to acts like plus a term that contains elements in V ?

]]>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.

]]>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)

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

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

]]>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?

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