Symmetric monoidal structure on cosimplicial spaces - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T01:07:29Z http://mathoverflow.net/feeds/question/42912 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/42912/symmetric-monoidal-structure-on-cosimplicial-spaces Symmetric monoidal structure on cosimplicial spaces Toribio Smith 2010-10-20T16:52:34Z 2010-11-08T17:30:03Z <p>Is there a monoidal structure on the category $Spc^{\Delta}$ of cosimplicial spaces such that in the adjunction $$\Delta^{\bullet}\otimes-\colon Spc\leftrightarrows Spc^{\Delta}\colon Tot(-)$$ the left adjoint is (strong) symmetric monoidal? If this is true, can it be generalized by replacing $Spc$ by any symmetric monoidal category?</p>