Geodesic
Stable tubes in extriangulated categories
Czechoslovak Mathematical Journal, Tome 72 (2022) no. 3, pp. 765-782
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Let $\mathcal {X}$ be a semibrick in an extriangulated category. If $\mathcal {X}$ is a $\tau $-semibrick, then the Auslander-Reiten quiver $\Gamma (\mathcal {F}(\mathcal {X}))$ of the filtration subcategory $\mathcal {F}(\mathcal {X})$ generated by $\mathcal {X}$ is $\mathbb {Z}\mathbb {A}_{\infty }$. If $\mathcal {X}=\{X_{i}\}_{i=1}^{t}$ is a $\tau $-cycle semibrick, then $\Gamma (\mathcal {F}(\mathcal {X}))$ is $\mathbb {Z}\mathbb {A}_{\infty }/\tau _{\mathbb {A}}^{t}$.
Let $\mathcal {X}$ be a semibrick in an extriangulated category. If $\mathcal {X}$ is a $\tau $-semibrick, then the Auslander-Reiten quiver $\Gamma (\mathcal {F}(\mathcal {X}))$ of the filtration subcategory $\mathcal {F}(\mathcal {X})$ generated by $\mathcal {X}$ is $\mathbb {Z}\mathbb {A}_{\infty }$. If $\mathcal {X}=\{X_{i}\}_{i=1}^{t}$ is a $\tau $-cycle semibrick, then $\Gamma (\mathcal {F}(\mathcal {X}))$ is $\mathbb {Z}\mathbb {A}_{\infty }/\tau _{\mathbb {A}}^{t}$.
DOI : 10.21136/CMJ.2022.0145-21
Classification : 18E05
Keywords: extriangulated category; semibrick; Auslander-Reiten quiver 
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Wang, Li; Wei, Jiaqun; Zhang, Haicheng. Stable tubes in extriangulated categories. Czechoslovak Mathematical Journal, Tome 72 (2022) no. 3, pp. 765-782. doi: 10.21136/CMJ.2022.0145-21

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