Let $A$ be a module, $P$ be a chain complex of projective modules, $Q$ its subcomplex. Moreover, let $C$ be a resolution of the chain complex $A[0]$ (that is $(A[0])_0=A$ and $(A[0])_n=0$ otherwise; also we have a quasi-isomorphism $C\xrightarrow\sim A[0]$).
Given the following diagram
why is there a chain map $P\to C$ (such that the diagram commutes)?
I can handle situations if I have only triangles, but I don't see how to make the whole diagram to commute...