most recent 30 from http://mathoverflow.net 2013-05-24T22:17:00Z http://mathoverflow.net/feeds/user/4732 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/17569/a-model-structure-on-symmetric-monoidal-categories/18673#18673 Tony Elmendorf 2010-03-18T22:13:59Z 2010-03-18T22:13:59Z

<p>One basic problem is that the category of symmetric monoidal categories isn't complete. Its completion, in a basic sense, is the category of multicategories, on which it seems reasonable to conjecture there is a model category structure whose homotopy category "is" the connective part of stable homotopy -- we hope to prove this soon. See Elmendorf and Mandell, "Permutative categories, multicategories, and algebraic K-theory", which just appeared in Algebraic and Geometric Topology.</p>

http://mathoverflow.net/questions/3154/1-categorical-description-of-equivariant-homotopy-theory/5846#5846 Tony Elmendorf 2010-05-18T16:31:03Z 2010-05-18T16:31:03Z

Mark, the paper of mine you're remembering is the one joint with Peter May, &quot;Algebras over equivariant sphere spectra&quot;, JPAA 116 (1997) 139-149. It shows that, indeed, you can consider just one underlying category of G-spectra with a number of (cofibrantly generated) model structures on it. The &quot;change of universe&quot; functors usually considered from the Lewis-May-Steinberger point of view are then simply the derived functors of the identity functor. The category itself is the EKMM category with G acting in the obvious way on the objects. -- Tony Elmendorf