Derived functor and natural transformation

64 Views Asked by At

Let $A$ and $B$ be two categories.

Let $F_1, F_2$ be functors from $A$ to $B$ and there is a natural transformation $\eta$ from $F_1$ to $F_2$.

Now let $G$ be another functor from $B$ to $B$.

Now, there is a natural transformation from $R^iG \circ F_1$ to $R^iG \circ F_2$. Why does this map through $R^i(G \circ F_1)$, i.e it can be written as $R^iG \circ F_1 \to R^i(G \circ F_1) \to R^iG \circ F_2$?