Later takes a limit over smaller indices. Dually, the earlier modality takes a colimit over larger indices: an element of $⊲𝑃$ at $𝑥$ is a $𝑃$-element sitting at some object $𝑦$ strictly above $𝑥$, carried down along a chosen morphism $𝑥\to 𝑦$.

Earlier is left adjoint to later:

Under this adjunction, $\text{𝗇𝖾𝗑𝗍}:𝑃\to ⊳𝑃$ corresponds to

.