The singular Yoneda category and the stabilization functor

For a noetherian ring \(\Lambda \), the stabilization functor yields an embedding of the singularity category of \(\Lambda \) into the homotopy category of acyclic complexes of injective \(\Lambda \)-modules. When \(\Lambda \) contains a semisimple artinian subring E, we give an explicit description of the stabilization functor using the Hom complexes in the E-relative singular Yoneda dg category of \(\Lambda \). As an application to an artin algebra, we obtain an explicit compact generator for the mentioned homotopy category, whose dg endomorphism algebra turns out to be quasi-isomorphic to the associated dg Leavitt algebra.