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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeDec 23rd 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added to the Examples at [[structured (infinity,1)-topos]] a section <a href="http://nlab.mathforge.org/nlab/show/structured+(infinity%2C1)-topos#CanonicalStructureSheafOnObjectsInBigTopos">Canonical structure sheaves on objects in a big topos</a>. For the moment this only contains the observation that for $\mathbf{H} = Sh(\mathcal{G})$ the big topos on a geometry $\mathcal{G}$, for every object $X \in \mathbf{H}$ its little topos $\mathbf{H}/X$ is canonically equipped with a $\mathcal{G}$-structure sheaf. This is evident from the discussion at [[etale geometric morphism]], but it nevertheless seems to be noteworthy. I have added also an inducation on how this canonical structure sheaf is indeed that of $\mathcal{G}$-valued functions on $X$. But more details on this would be desireable. But I have to interrupt now.

   I have added to the Examples at structured (infinity,1)-topos a section Canonical structure sheaves on objects in a big topos.

   For the moment this only contains the observation that for $\mathbf{H} = Sh(\mathcal{G})$ the big topos on a geometry $\mathcal{G}$, for every object $X \in \mathbf{H}$ its little topos $\mathbf{H}/X$ is canonically equipped with a $\mathcal{G}$-structure sheaf.

   This is evident from the discussion at etale geometric morphism, but it nevertheless seems to be noteworthy.

   I have added also an inducation on how this canonical structure sheaf is indeed that of $\mathcal{G}$-valued functions on $X$. But more details on this would be desireable. But I have to interrupt now.