Geodesic
One-sided Gorenstein subcategories
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 483-504 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We introduce the right (left) Gorenstein subcategory relative to an additive subcategory $\mathscr {C}$ of an abelian category $\mathscr {A}$, and prove that the right Gorenstein subcategory $r\mathcal {G}(\mathscr {C})$ is closed under extensions, kernels of epimorphisms, direct summands and finite direct sums. When $\mathscr {C}$ is self-orthogonal, we give a characterization for objects in $r\mathcal {G}(\mathscr {C})$, and prove that any object in $\mathscr {A}$ with finite $r\mathcal {G}(\mathscr {C})$-projective dimension is isomorphic to a kernel (or a cokernel) of a morphism from an object in $\mathscr {A}$ with finite $\mathscr {C}$-projective dimension to an object in $r\mathcal {G}(\mathscr {C})$. As an application, we obtain a weak Auslander-Buchweitz context related to the kernel of a hereditary cotorsion pair in $\mathscr {A}$ having enough injectives.
We introduce the right (left) Gorenstein subcategory relative to an additive subcategory $\mathscr {C}$ of an abelian category $\mathscr {A}$, and prove that the right Gorenstein subcategory $r\mathcal {G}(\mathscr {C})$ is closed under extensions, kernels of epimorphisms, direct summands and finite direct sums. When $\mathscr {C}$ is self-orthogonal, we give a characterization for objects in $r\mathcal {G}(\mathscr {C})$, and prove that any object in $\mathscr {A}$ with finite $r\mathcal {G}(\mathscr {C})$-projective dimension is isomorphic to a kernel (or a cokernel) of a morphism from an object in $\mathscr {A}$ with finite $\mathscr {C}$-projective dimension to an object in $r\mathcal {G}(\mathscr {C})$. As an application, we obtain a weak Auslander-Buchweitz context related to the kernel of a hereditary cotorsion pair in $\mathscr {A}$ having enough injectives.
DOI : 10.21136/CMJ.2019.0385-18
Classification : 16E10, 18G10, 18G25
Keywords: right Gorenstein subcategory; self-orthogonal subcategory; relative projective dimension; cotorsion pair; kernel; (weak) Auslander-Buchweitz context 
@article{10_21136_CMJ_2019_0385_18,
     author = {Song, Weiling and Zhao, Tiwei and Huang, Zhaoyong},
     title = {One-sided {Gorenstein} subcategories},
     journal = {Czechoslovak Mathematical Journal},
     pages = {483--504},
     year = {2020},
     volume = {70},
     number = {2},
     doi = {10.21136/CMJ.2019.0385-18},
     mrnumber = {4111855},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0385-18/}
}
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Song, Weiling; Zhao, Tiwei; Huang, Zhaoyong. One-sided Gorenstein subcategories. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 483-504. doi: 10.21136/CMJ.2019.0385-18

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