A note on singular equivalences (Q2037711)

For an exact sequence \(0\to \mathcal{A} \to \mathcal{B} \stackrel{e}{\to} \mathcal{C}\to 0\) of abelian categories such that \(\mathcal{B}\) and \(\mathcal{C}\) have enough projective objects, the authors give equivalent conditions for \(D^b_{\mathrm{sg}}(e): D^b_{\mathrm{sg}}(\mathcal{B}) \to D^b_{\mathrm{sg}}(\mathcal{C})\) inducing a singular equivalence. This generalizes the main theorem of \textit{X.-W. Chen} [Proc. Am. Math. Soc. 142, No. 8, 2633--2640 (2014; Zbl 1309.18010)].