AI 中文总结
本文通过3顶点有向DG箭图构造无穷多个互不等价的幻影范畴，并利用固定有限维DG代数重分配次数实现这些范畴。
AI 中文摘要
我们从具有3个顶点的具体有向DG箭图构造了无穷多对两两非导出-Morita-等价的幻影范畴 $\mathcal{P}_{m}, m\in\mathbb{Z}$。此外，存在一个固定的有限维DG代数 $C$，使得对每个 $m\in\mathbb{Z}$，有一种方法在不改变微分的情况下重新分配 $C$ 上的上同调次数，得到一个新的DG代数 $C_{m}$，且满足 $\mathrm{Perf}(C_{m})\cong \mathcal{P}_{m}$。
英文摘要
We construct infinitely many pairwise non-derived-Morita-equivalent phantom categories $\mathcal{P}_{m}, m\in\mathbb{Z}$ from concrete directed DG quivers with 3 vertices. Moreover, there exists a fixed finite-dimensional DG algebra $C$ such that for each $m\in\mathbb{Z}$, there is a way to reassign cohomological gradings on $C$ (without changing the differential) to obtain a new DG algebra $C_{m}$ with $\mathrm{Perf}(C_{m})\cong \mathcal{P}_{m}$.
