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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMar 16th 2012
   • (edited Mar 16th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexGiven a topos $\mathcal{T}$, and an [[internal site]] $\mathbb{C} \in Cat(\mathcal{T})$, there should be a nice way to describe the topos of internal sheaves on $\mathbb{C}$ in terms of morphisms in $\hat Cat(\mathcal{T})$ (the 2-category of large categories in $\mathcal{T}$, being some sub-2-category of [[2-sheaves]] in $Func(\mathcal{T}^op, \hat Cat)$) from $\mathbb{C}^{op}$ to the [[codomain fibration]] / self-indexing $\mathbb{T}$ of $\mathcal{T}$, i.e. regarding an internal sheaf as a morphism $\mathbb{C}^{op} \to \mathbb{T}$ in $\hat Cat(\mathcal{T})$. This should be obvious. But is there a nice discussion from this point of view somewhere in the literature?

   Given a topos $\mathcal{T}$, and an internal site $\mathbb{C} \in Cat(\mathcal{T})$, there should be a nice way to describe the topos of internal sheaves on $\mathbb{C}$ in terms of morphisms in $\hat Cat(\mathcal{T})$ (the 2-category of large categories in $\mathcal{T}$, being some sub-2-category of 2-sheaves in $Func(\mathcal{T}^op, \hat Cat)$) from $\mathbb{C}^{op}$ to the codomain fibration / self-indexing $\mathbb{T}$ of $\mathcal{T}$, i.e. regarding an internal sheaf as a morphism $\mathbb{C}^{op} \to \mathbb{T}$ in $\hat Cat(\mathcal{T})$.

   This should be obvious. But is there a nice discussion from this point of view somewhere in the literature?

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeMar 16th 2012
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   Author: Mike Shulman
   Format: MarkdownItexB2.3.13?

   B2.3.13?

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMar 16th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexAh! :-)

   Ah! :-)

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMar 16th 2012
   • (edited Mar 16th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexOkay, so I was looking for such a pointer to include in the new entry [[internal sheaf]]. But I'll announce this in another thread... [here](http://nforum.mathforge.org/discussion/3688/internal-sheaf/).

   Okay, so I was looking for such a pointer to include in the new entry internal sheaf. But I’ll announce this in another thread… here.