On coherent topoi & coherent $1$-localic $\mathrm{\infty }$-topoi

In this note we prove the following useful fact that seems to be missing from the literature: the $\mathrm{\infty }$-category of coherent ordinary topoi (in the sense of SGA4) is equivalent to the $\mathrm{\infty }$-category of coherent $1$-localic $\mathrm{\infty }$-topoi (in Lurie’s sense). We also collect a number of examples of coherent geometric morphisms between $\mathrm{\infty }$-topoi coming from algebraic geometry.