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I'd like to write something about a Quillen equivalence, if any, between model structures on
n-connected pointed spaces
grouplike E-n spaces .
With the equivalence given by forming n-fold look spaces.
But I need more input. I found a nice discussion of a model structure on n-connected pointed spaces in A closed model category on (n-1)-connected spaces. I suppose there is a standard model structure on E-k algebras in Top. Is a Quilen equivalence described anywhere?
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