The singular Yoneda category and the stabilization functor

For a noetherian ring \(\Lambda \) $\mathrm{\Lambda }$ , the stabilization functor yields an embedding of the singularity category of \(\Lambda \) $\mathrm{\Lambda }$ into the homotopy category of acyclic complexes of injective \(\Lambda \) $\mathrm{\Lambda }$ -modules. When \(\Lambda \) $\mathrm{\Lambda }$ 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 \(\Lambda \) $\mathrm{\Lambda }$ . 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.