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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.
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
wrote section Alexander-Whitney and shuffle morphisms
(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.)
Ah, clever of you! I'm sorry if I bothered you.
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.
am in the process of restructuring, polishing and expanding monoidal Dold-Kan correspondence.
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)
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.
I have added at monoidal Dold-Kan correspondence the missing reference
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.
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.
Thanks, Zoran.
I looked at his page. But I cannot find that particular article.
Try here
Thanks!!
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