The homological theory of quasi-resolving subcategories
In [Mem. Am. Math. Soc. 94, 146 p. (1969; Zbl 0204.36402)], \textit{M. Auslander} and \textit{M. Bridger} introduced the notion of resolving subcategories, capturing the behaviour of several natural subcategories of module categories in this notion. The starting point of the article under review is the observation that the nice homological behaviour of resolving subcategories extends also to setups where the definition does not apply. Xiaosheng Zhu then proceeds to remedy this situation, generalising the definition of resolving subcategories by introducing ``quasi-resolving subcategories''. (Essentially the generation-assumption is weakened, and it is only required that the projectives inside the subcategory generate the subcategory.) It is shown that many homological properties of resolving subcategories extend naturally to this more general notion.
scientific article; zbMATH DE number 6338797
scientific article