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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeMay 18th 2012
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexThe preprint [The homotopy theory of coalgebras over a comonad](http://arxiv.org/abs/1205.3979) by Hess and Shipley looks interesting. Among other things it contains * a theorem about replacing a model structure by a Quillen equivalent one in which the cofibrations are the monomorphisms * a theorem about when the category of coalgebras for a comonad inherits a model structure by "left transfer". I wonder whether there could be a model structure on coalgebraically cofibrant objects?

   The preprint The homotopy theory of coalgebras over a comonad by Hess and Shipley looks interesting. Among other things it contains

   • a theorem about replacing a model structure by a Quillen equivalent one in which the cofibrations are the monomorphisms
   • a theorem about when the category of coalgebras for a comonad inherits a model structure by “left transfer”.

   I wonder whether there could be a model structure on coalgebraically cofibrant objects?

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 18th 2012
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   Author: Urs
   Format: MarkdownItexAh, thanks for pointing this out. I had heard them [speak](http://golem.ph.utexas.edu/category/2011/02/structured_ring_spectra_2011.html#c039003) about that, but didn't see the article appear.

   Ah, thanks for pointing this out. I had heard them speak about that, but didn’t see the article appear.