Given a topos $E$, the subobject classifier $Ω_E$ is known to be the initial internal frame. On the other hand, the unique frame morphism $i:{Ω_E}\rightarrow{H}$ is known to have a right adjoint $τ$ as the classifying map of the top over $H$ (see Topos Semantics for Higher-Order Modal Logic. S Awodey, K Kishida, HC Kotzsch. arXiv:1403.0020). The resulting comonad $i\circτ$ models the S4 system of Modal Logic.