# ct.category theory – Does a natural transformation of functors induce a natural transformation between their right adjoints?

Let $$mathcal{C}$$ and $$mathcal{D}$$ be two categories and $$F$$ and $$G: mathcal{C}to mathcal{D}$$ be two functors. Suppose $$F$$ and $$G$$ have right adjoints $$F^{wedge}$$ and $$G^{wedge}: mathcal{D}to mathcal{C}$$.

Now let $$T:FRightarrow G$$ be a natural transformation.

My question is: does $$T$$ induce a natural transformation $$T^{wedge}:G^{wedge}Rightarrow F^{wedge}$$?