Synthetic topos theory
[000O] Definition

Let UU be a universe. The action of Sh:(Topos(U))opLogos(U)\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 fff\mapsto {f}^{*}. We call f{f}^{*} the inverse image of a morphism ff of UU-toposes.