Let ${𝒜}$ be an abelian category and ${𝒳},{𝒞}$ be two quasi-resolving subcategories of ${𝒜}$, where ${𝒞}$ is closed under direct summands and ${𝒞}$ is a cogenerator for ${𝒳}$. For any $M\in {{𝒳}}^{{\perp }_1}$, it is shown that ${𝒳}$-$pd(M)={𝒞}$-$pd(M)$. Some examples and applications are also given.

中文翻译：

---

解析分辨率尺寸的注意事项

让${𝒜}$是一个阿贝尔范畴并且${𝒳},{𝒞}$是两个准解析子类别${𝒜}$， 在哪里${𝒞}$在直接命令下关闭，并且${𝒞}$是一个热电联供装置${𝒳}$. 对于任何$米\in {{𝒳}}^{{\perp }_1}$, 表明${𝒳}$-$PD(米)={𝒞}$-$PD(米)$. 还给出了一些例子和应用。