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For questions about sheaves on a topological space.

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Pullback of a constant sheaf over arbitrary sites

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?
Arun Kumar's user avatar