Left Kan extension (${\mathrm{Lan}}_{F}Q$)

The left Kan extension of $Q:\mathcal{C}\to \mathcal{E}$ along $F:\mathcal{C}\to \mathcal{D}$ is universal among functors on $\mathcal{D}$ equipped with a transformation from $Q$ to their restriction along $F$. When it exists, it is left adjoint to precomposition. For small indexing categories and cocomplete $\mathcal{E}$, it is computed by comma-category colimits.