In Wikipedia's article on Kan extensions 1, in the view of Kan extensions as colimits, I am confused about the notation: $(Lan_F X)(b) = \varinjlim_{f:Fa \to b} X(a)$.

Wikipedia says that the colimit is over the category $F \downarrow b$, but the functor $X$ is from $\mathbf{A}$ to $\mathbf{C}$. I am a bit confused about this, I understand that the functor "inside" the colimit notation should be defined over the category where we are taking it. Is there any place where I can read about this limit/colimit notation?