Cotorsion pairs induced by duality pairs
\textit{L. L.\ Avramov} and \textit{H.-B.\ Foxby} [Proc.\ Lond. Math.\ Soc., III. Ser. 75, 241--270 (1997; Zbl 0901.13011)] and \textit{L. W.\ Christensen} [Trans.\ Am.\ Soc.\ 353, No. 5, 1839--1883 (2001; Zbl 0969.13006)] demonstrated how a semidualizing complex \(C\) over a commutative ring \(R\) gives rise to the so-called Auslander class \(A^C_0\) and the Bass class \(B^C_0\). The authors introduce \textit{duality pairs} parts of which are \(A^C_0\) and \(B^C_0\) and show how the left of such a pair is covering and preenveloping. Then, a result of \textit{E. E. Enochs} and \textit{H. Holm} [Isr. J.\ Math.\ 174, 253--268 (2009; Zbl 1184.13029)] on Auslander and Bass classes is generalized: \textit{the class of Gorenstein injective modules is covering when the ground ring has a dualizing complex.}
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