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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJan 12th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave created an entry [[homotopy dimension]]

   have created an entry homotopy dimension

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJan 12th 2011
   • (edited Jan 12th 2011)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have spelled out at [[homotopy dimension]] the proof that the $\infty$-presheaf topos on a site with terminal object has homotopy dimension $\leq 0$. And I have made explicit that the argument straightforwardly generalizes to imply that every [[local (infinity,1)-topos]] has homotopy dimension $\leq 0$. This implies a whole chain of immediate pleasant results: * every local $\infty$-topos is * of cohomology dimension $\leq 0$ * and hypercomplete; hence * every [[cohesive (infinity,1)-topos]] is * of cohomology dimension $\leq 0$ * and hypercomplete.

   I have spelled out at homotopy dimension the proof that the $\infty$-presheaf topos on a site with terminal object has homotopy dimension $\leq 0$. And I have made explicit that the argument straightforwardly generalizes to imply that every local (infinity,1)-topos has homotopy dimension $\leq 0$.

   This implies a whole chain of immediate pleasant results:

   • every local $\infty$-topos is

     • of cohomology dimension $\leq 0$

     • and hypercomplete;

   hence

   • every cohesive (infinity,1)-topos is

     • of cohomology dimension $\leq 0$

     • and hypercomplete.