Corollary 6.89.
Let \(\phi_*\colon T_1 \to T_2\) be an essential morphism of topoi. Then \(\phi_\sharp\colon T_1 \to T_2\) sends objects of constant shape in \(T_1\) to objects of constant shape in \(T_2\).
Higher Topos Theory Section 6.6: Essential morphisms and shape theory
Corollary 6.89.
Let \(\phi_*\colon T_1 \to T_2\) be an essential morphism of topoi. Then \(\phi_\sharp\colon T_1 \to T_2\) sends objects of constant shape in \(T_1\) to objects of constant shape in \(T_2\).