Summary: Let \(R\) be an Artin algebra and \(\mathcal C\) an additive subcategory of \(\mathrm{mod}(R)\). We construct a \(t\)-structure on the homotopy category \(\mathrm K^-(\mathcal C)\) and argue that its heart \(\mathcal H_{\mathcal C}\) is a natural domain for higher Auslander-Reiten (AR) theory. In the paper [E. Backelin and O. Jaramillo, J. Algebra 339, No. 1, 80-96 (2011; Zbl 1273.16015)] we showed that \(\mathrm K^-(\mathrm{mod}(R))\) is a natural domain for classical AR theory. Here we show that the abelian categories \(\mathcal H_{\mathrm{mod}(R)}\) and \(\mathcal H_{\mathcal C}\) interact via various functors. If \(\mathcal C\) is functorially finite then \(\mathcal H_{\mathcal C}\) is a quotient category of \(\mathcal H_{\mathrm{mod}(R)}\). We illustrate our theory with two examples:
When \(\mathcal C\) is a maximal \(n\)-orthogonal subcategory O. Iyama developed a higher AR theory, [see Adv. Math. 210, No. 1, 22-50 (2007; Zbl 1115.16005)]. In this case we show that the simple objects of \(\mathcal H_{\mathcal C}\) correspond to Iyama’s higher AR sequences and derive his higher AR duality from the existence of a Serre functor on the derived category \(\mathrm D^b(\mathcal H_{\mathcal C})\). The category \(\mathcal O\) of a complex semi-simple Lie algebra fits into higher AR theory in the situation when \(R\) is the coinvariant algebra of the Weyl group.