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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJan 12th 2011

have created an entry homotopy dimension

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeJan 12th 2011
• (edited Jan 12th 2011)

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