Given a geometric morphism between arbitrary Grothendieck topoi, $f:\mathcal{Sh(D)}\to\mathcal{Sh(C)}$, does the pullback $f^{-1}$ (i.e, the left adjoint) take constant sheafs to constant sheafs?
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6$\begingroup$ Depends on how you define constant sheaves, for me by definition, constant sheaves are the sheaves of the form $p^*(S)$ where $p$ is the unique geometric morphism $Sh(D) \rightarrow Set = Sh(*)$. So yes. $\endgroup$– Simon HenryCommented Mar 6, 2018 at 14:01
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$\begingroup$ Thanks! I was only looking at it as the sheafification of the constant presheaf, but your definition makes things more clear. $\endgroup$– Arun KumarCommented Mar 6, 2018 at 14:15
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$\begingroup$ For more discussion on this see SGA IV exp IV section 4.3 $\endgroup$– TomoCommented Apr 4, 2018 at 21:05
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