most recent 30 from http://mathoverflow.net 2013-05-25T03:34:35Z http://mathoverflow.net/feeds/question/80054 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/80054/a-kind-of-james-construction-for-infty-groupoids Colin Tan 2011-11-04T14:39:07Z 2011-11-08T08:37:52Z

<p>Start with a pointed $\infty$-groupoid $X$. Consider $X$ as a pointed $\infty$-category and construct the free <s>pointed</s> monoidal $\infty$-category $\bar{X}$. This free construction $\bar{X}$ is at least an $\infty$-groupoid too. How is the homotopy type of $\bar{X}$ related to the homotopy type of $X$?</p> <p>This seems to be a James construction in the context of $\infty$-groupoids, but I can't be sure. That is, conjecturally, $\bar{X}\simeq \Omega\Sigma X$.</p>

http://mathoverflow.net/questions/80054/a-kind-of-james-construction-for-infty-groupoids/80365#80365 dagness 2011-11-08T08:37:52Z 2011-11-08T08:37:52Z

<p>The isomorphism fS0B = S0A implies the equivalence fS0B ' S0A since S0B is qf-fibrant.</p>