Let $U$ be a universe. The action of $\mathord {\textnormal {\textsf {Sh}}}:{(\mathord {\textnormal {\textsf {Topos}}}(U))}^{\mathord {\textnormal {\textsf {op}}}}\simeq \mathord {\textnormal {\textsf {Logos}}}(U)$ on morphisms is also denoted by $f\mapsto {f}^{*}$. We call ${f}^{*}$ the inverse image of a morphism $f$ of $U$-toposes.