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We introduce the notion of balanced pair of additive subcategories in anabelian category. We give sufficient conditions under which the balanced pairof subcategories gives rise to equivalent homotopy categories of complexes. Asan application, we prove that for a left-Gorenstein ring, there exists atriangle-equivalence between the homotopy category of its Gorenstein projectivemodules and the homotopy category of its Gorenstein injective modules, whichrestricts to a triangle-equivalence between the homotopy category of projectivemodules and the homotopy category of injective modules. In the case ofcommutative Gorenstein rings we prove that up to a natural isomorphism ourequivalence extends Iyengar-Krause's equivalence.

Homotopy Equivalences induced by Balanced Pairs