The singular Yoneda category and the stabilization functor (Q6593025)

Let \(\Lambda\) be a noetherian ring. The stabilization functor yields an embedding of the singularity category of \(\Lambda\) into the homotopy category of acyclic complexes of injective \(\Lambda\)-modules. It is a triangulated analogue of the gluing functor in the DG setting [\textit{A. Kuznetsov} and \textit{V. A. Lunts}, Int. Math. Res. Not. 2015, No. 13, 4536--4625 (2015; Zbl 1338.14020)] and \(\infty\)-categorical setting [\textit{T. Dyckerhoff} et al., Int. Math. Res. Not. 2021, No. 20, 15733--15745 (2021; Zbl 1536.18016)]. When the ring is Gorenstein, it provides a functorial construction of complete injective resolutions. Generally, it is difficult and meaningful to describe the stabilization functor explicitly. When \(\Lambda\) contains a semi-simple Artinian subring \(E\), an explicit description of the stabilization functor using the Hom complexes in the \(E\)-relative singular Yoneda DG category of \(\Lambda\) is given in the paper. Using it, the authors get and explicit compact generator for the mentioned homotopy category, whose DG endomorphism algebra turns out to be quasi-isomorphic to the associated DG Leavitt algebra.