Suppose $\mathcal{A,B,C}$ are additive categories, $\mathcal B$ is a subcategory of $\mathcal C$. Now let $F,G: \mathcal A\rightarrow\mathcal B$ be two additive functors. Suppose $F,G$ are naturally equivalent as functors $\mathcal{A}\rightarrow\mathcal C$, do they induce the same map $K_n(\mathcal A)\rightarrow K_n(\mathcal B)$? Of course, $\mathcal{A,B,C}$ are endowed with the split exact structures. Thanks!
