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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMar 16th 2012
• (edited Mar 16th 2012)

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

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

• CommentRowNumber2.
• CommentAuthorMike Shulman
• CommentTimeMar 16th 2012

B2.3.13?

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMar 16th 2012

Ah! :-)

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeMar 16th 2012
• (edited Mar 16th 2012)

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.