Let R be a commutative Noetherian local ring with residue field k. Let be a resolving subcategory of finitely generated R-modules. This paper mainly studies when contains k or consists of totally reflexive modules. It is proved that does so if is closed under cosyzygies. A conjecture of Dao and Takahashi is also shown to hold in several cases.
"Resolving Subcategories Closed Under Certain Operations and a Conjecture of Dao and Takahashi." Michigan Math. J. 70 (2) 341 - 367, May 2021. https://doi.org/10.1307/mmj/1592359276