# Extension groups in quotient categories

Let $$\mathcal{A}$$ be an abelian category and let $$\mathcal{B}$$ be a Serre subcategory of $$\mathcal{A}$$. We can form the quotient category $$\mathcal{A}/\mathcal{B}$$, and the canonical functor $$Q:\mathcal{A}\to \mathcal{A}/\mathcal{B}$$ is exact. As such, given $$X$$ and $$Y$$ two objects in $$\mathcal{A}$$, there is a group morphism $$q:\operatorname{Ext}^1_{\mathcal{A}}(X,Y)\to \operatorname{Ext}^1_{\mathcal{A}/\mathcal{B}}(Q(X),Q(Y))$$ induced by $$Q$$ on the extension groups. Do we know something on the image or the kernel of $$q$$?