Consider a site $(\mathcal C,J)$ and the category of sheaves $\mathscr S=\mbox{Sh}(\mathcal C,J)$ on it. Given a morphism $f:X\rightarrow Y$ between sheaves, when is the pullback funtor $f^*:\mathscr S/Y\rightarrow\mathscr S/X$ monadic? And what if I consider sheaves valued in a generic complete category $\mathcal A$ (instead of $\mathbf{Set}$)?
2026-02-24 00:05:57.1771891557
When the pullback functor is monadic
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