Stable tubes in extriangulated categories

summary: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 $\mathbb {Z}\mathbb {A}_{\infty }/\tau _{\mathbb {A}}^{t}$