[000O] DefinitionLet UUU be a universe. The action of Sh:(Topos(U))op≃Logos(U)\mathord {\textnormal {\textsf {Sh}}}:{(\mathord {\textnormal {\textsf {Topos}}}(U))}^{\mathord {\textnormal {\textsf {op}}}}\simeq \mathord {\textnormal {\textsf {Logos}}}(U)Sh:(Topos(U))op≃Logos(U) on morphisms is also denoted by f↦f∗f\mapsto {f}^{*}f↦f∗. We call f∗{f}^{*}f∗ the inverse image of a morphism fff of UUU-toposes.