Left Kan extension: switching K and F If $F:  ⟶ $ and $K:  ⟶ ℰ$ are functors, where $$ is small and both $$ and $ℰ$ are cocomplete. How do the left Kan extension of $F$ along $K$ (${\rm Lan}_K(F)$) and the left Kan extension of $K$ along $F$ (${\rm Lan}_F(K)$) relate with one another? (Is it safe to say that they are adjoints for example?)
EDIT: Actually, I asked the question in general but what I had in mind was the special case where $K := y:  ⟶ \widehat{}$ is the Yoneda embedding, so any tip to show that ${\rm Lan}_y(F) ⊣ {\rm Lan}_F(y)$ (or that ${\rm Lan}_F(y) \cong N_F := Hom(F(-), -)$) would be helpful as well.
Any insight on this would be very much appreciated!

If $y : A \to[A°,Set]$ is the Yoneda embedding it is a general fact that, given a functor $f : A \to B$, there is the adjunction
$$
Lan_yf \dashv Lan_fy
$$ this is called nerve-realization paradigm.
As you can see e.g. here, asking that the two functors $F,K$ are related in this way is a rather strong request (in fact, the tentative proof in the answer contains a flaw, and to this day no convincing example, different than Yoneda extensions, has been given)
