Applications of resolving subcategories to singularity categories and monomorphism categories

作者：Gao, Nan; Song, Keyan; You, Hanyang^*; Zhou, Guodong

来源：JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2023.

DOI：10.1142/S0219498825501142

• Left perpendicular category
• monomorphism category
• resolution theorem for derived categories
• resolving category
• singularity category

In this paper, we study resolving subcategories and singularity categories. First, if the left perpendicular category of a module T over an Artin algebra A is the additive closure of another module M, then the singularity category of A and that of the endomorphism algebra EndA(M) of M are closed related. This gives a categorical version of a recent result of Zhang ([31], Theorem 2]). Second, we apply the resolution theorem for derived categories to elliptic curves, the monomorphism subcategory of a Gorenstein algebra and of a kind of Eilenberg-Moore category. As consequences, their singularity categories are equivalent, which explains why monomorphism categories are closely related to singularity categories.

• 单位
  杭州师范大学; 西南大学; 上海大学