Let \(\mathcal {A}\) be an abelian category with enough projective objects, and let \(\mathcal {X}\) be a quasi-resolving subcategory of \(\mathcal {A}\). In this paper, we investigate the affinity of the Spanier–Whitehead category \(\mathsf {SW}(\mathcal {X})\) of the stable category of \(\mathcal {X}\) with the singularity category \(\mathsf {D}_{\mathsf {sg}}(\mathcal {A})\) of \(\mathcal {A}\). We construct a fully faithful triangle functor from \(\mathsf {SW}(\mathcal {X})\) to \(\mathsf {D}_{\mathsf {sg}}(\mathcal {A})\), and we prove that it is dense if and only if the bounded derived category \(\mathsf {D}^{\mathsf {b}}(\mathcal {A})\) of \(\mathcal {A}\) is generated by \(\mathcal {X}\). Applying this result to commutative rings, we obtain characterizations of the isolated singularities, the Gorenstein rings and the Cohen–Macaulay rings. Moreover, we classify the Spanier–Whitehead categories over complete intersections. Finally, we explore a method to compute the (Rouquier) dimension of the triangulated category \(\mathsf {SW}(\mathcal {X})\) in terms of generation in \(\mathcal {X}\).

令\（\ mathcal {A} \）为具有足够投影对象的阿贝尔类别，令\（\ mathcal {X} \）为\（\ mathcal {A} \）的拟解析子类别。在本文中，我们研究了\（\ mathcal {X} \）的稳定类别的Spanier–Whitehead类别\（\ mathsf {SW}（\ mathcal {X}）\）与奇异类别\（ \（\ mathcal {A} \）的\ mathsf {D} _ {\ mathsf {sg}}（\ mathcal {A}）\）。我们从\（\ mathsf {SW}（\ mathcal {X}）\）到\（\ mathsf {D} _ {\ mathsf {sg}}（\ mathcal {A}）\）构造一个完全忠实的三角函子，并且我们证明，当且仅当有界派生类别时，它是密集的\（\ mathsf {d} ^ {\ mathsf {B}}（\ mathcal {A}）\）的\（\ mathcal {A} \）通过产生\（\ mathcal {X} \）。将这个结果应用到交换环，我们得到了孤立奇点，Gorenstein环和Cohen-Macaulay环的特征。此外，我们在完整的交叉路口上对Spanier-Whitehead类别进行了分类。最后，我们探索的方法来计算三角范畴的（Rouquier）尺寸\（\ mathsf {SW}（\ mathcal {X}）\）在产生方面\（\ mathcal {X} \） 。