Avramov-Martsinkovsky type exact sequences for extriangulated categories
英文摘要：
Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an extriangulated category with a proper class $ξ$ of $\mathbb{E}$-triangles. In this paper, we first introduce the $ξ$-Gorenstein cohomology in terms of $ξ$-$\mathcal{G}$projective resolutions and $ξ$-$\mathcal{G}$injective coresolutions, respectively, and then we get the balance of $ξ$-Gorenstein cohomology. Moreover, we study the interplay among $ξ$-cohomology, $ξ$-Gorenstein cohomology and $ξ$-complete cohomology, and obtain the Avramov-Martsinkovsky type exact sequences in this setting.
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