Left Kan extension
= Left Kan extension
{title2=$\operatorname{Lan}_F Q$}
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.