I read the article "The Homological Theory of maximal cohen-macaulay approximations" wrote by Auslander and Buchweitz. In this article in Lemma 3.1 in category theory drew commutative diagram by two exact sequence $$0 \rightarrow Y_A \rightarrow X_A \rightarrow A \rightarrow 0$$ such that above exact sequence is X-approximaion of $A$ and $$0 \rightarrow A \rightarrow B \rightarrow C \rightarrow 0$$ and since $$Ext^1(C,X_A) \rightarrow Ext^1(C,A)$$ is an isomorphism, there exist an exact commutative diagram like:

My questions are these: How to calculate Z? Is it a pull back or push out? Can anybody help me please? thanks