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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 18th 2009

the invaluable Denis-Charles Cisinski provided a useful reference with a bit on cosimplicial algebras at MO (here). I added that reference to monoidal Dold-Kan correspondence and to cosimplicial algebra.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeNov 18th 2009

I restructured monoidal Dold-Kan correspondence a bit, creating two big subsections, one on the simplicial, one on the cosimplicial version. Then I expanded the intro bit of the cosimoplicial section by this text

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeNov 18th 2009
• CommentRowNumber4.
• CommentAuthorzskoda
• CommentTimeNov 20th 2009
• (edited Nov 20th 2009)
* Pavol Ševera, Thomas Willwacher, _Equivalence of formalities of the little discs operad_, [arXiv:0905.1789](http://arxiv.org/abs/0905.1789)

there is Appendix A: Compatibility of Alexander-Whitney map with products

which may be useful to further improve our entry.
• CommentRowNumber5.
• CommentAuthorTobyBartels
• CommentTimeNov 21st 2009
• (edited Nov 21st 2009)

(Zoran, I think that you may have lost your formatting again; check the buttons below the comment box and select ‘Markdown’ to make the bullet point, italics, and link work as you intended.)

• CommentRowNumber6.
• CommentAuthorzskoda
• CommentTimeNov 21st 2009
Thanks Toby for the hint. Though this time I wanted as it is. It is informative, the link is working, and it can be cut and paste into any entry in nlab as it is: I did not have time to include it in nlab and wanted Urs to pay attention to the reference if he does not already find it trivial mathematically and pedagogically.
• CommentRowNumber7.
• CommentAuthorTobyBartels
• CommentTimeNov 21st 2009

Ah, clever of you! I'm sorry if I bothered you.

• CommentRowNumber8.
• CommentAuthorzskoda
• CommentTimeNov 29th 2009

Not at all! Though I did not use it this time, your remarks are often useful to remember for future, to equip me to a more power-level than where I am, web-ignorant in comparison to you. Finally I included the reference in nlab, it seems Urs did not find anything new for him from the reference. In light of Baez's post maybe somebody who knows should create an entry about Frobenius monoidal functors.

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeNov 3rd 2010

am in the process of restructuring, polishing and expanding monoidal Dold-Kan correspondence.

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeNov 3rd 2010

inserted the proof of the Quillen equivalence between simplicial $k$-algebras and connective dg-k-algebras here

(this uses the strong theorem at monoidal Quillen adjunction, the proof of which I turn to now)

• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeNov 4th 2010
• (edited Nov 4th 2010)

I started a list of different flavors of Quillen equivalences for monoidal DK in a new section Summary

is it true that the only published reference for the Quillen equivalence

• connected simplicial commutative $k$-algebras $\simeq$ connected commutative dg-$k$-algebras

for $k$ of characteristic 0

is the remark on p. 223 of Quillen’s 1969 Rational homotopy theory

??

That seems hard to believe.

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeJan 21st 2011
• (edited Jan 21st 2011)

I have added at monoidal Dold-Kan correspondence the missing reference

• V.A. Hinich, V.V. Schechtman, Homotopy limits of homotopy algebras , in K-theory, arithmetic and geometry, Lecture Notes in Mathematics 1289, Springer, Berlin 240 − 264.

This is about the case that is currently not discussed at the entry: the equivalence of commutative COsimplicial algebras and commutative dg-algebra in non-neg degree over a field of char 0 (we have the commutative simplicial case and the non-commutative cosimplicial one, but not the commutative cosimplicial case).

Could someone maybe send me the pdf copy of that article, available online for those with subscription? I am currently not in Utrecht and it seems that Hamburg has canceled my VPN client account.

• CommentRowNumber13.
• CommentAuthorzskoda
• CommentTimeJan 21st 2011
• (edited Jan 21st 2011)

I am in a hurry to get to the bus, but I think that it can be found in the directorium from the Hinich’s homepage. I have that file somewhere, but look for his webpage, I can not search for it now.

• CommentRowNumber14.
• CommentAuthorUrs
• CommentTimeFeb 8th 2011

Thanks, Zoran.

I looked at his page. But I cannot find that particular article.

• CommentRowNumber15.
• CommentAuthorzskoda
• CommentTimeFeb 8th 2011

Try here

• CommentRowNumber16.
• CommentAuthorUrs
• CommentTimeFeb 8th 2011

Thanks!!