Koszul duality
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Cited by (113)
Generalized Koszul algebra and Koszul duality
2023, Journal of AlgebraCitation Excerpt :The Koszul rings in the sense of [BGS1] will be called sometimes classically Koszul later in this paper. The concept of Koszul algebras has been generalized to higher Koszul algebras [Ber,GMMZ,HY,Lü,LHL] and to categories [Man,BGS2,MOS], which are not the topics in this paper. A linear projective resolution of a graded module M can be characterized by the property of (the radical filtration of) syzygies of M [GM1, Proposition 3.1 and Lemma 5.1] (see Proposition 3.2).
Reduction techniques of singular equivalences
2022, Journal of AlgebraLadders of recollements of abelian categories
2021, Journal of AlgebraEventually homological isomorphisms in recollements of derived categories
2020, Journal of AlgebraCitation Excerpt :Owing to Corollary 1, we restrict our discussions to standard recollement in the following text. The idea of this definition comes from [1,3], where the concept “ladder” was introduced to study mixed categories. Obviously, a 1-recollement is nothing but a recollement, and a 2-recollement is a perfect recollement, that is, the two functors in the second layer preserve compactness (see [1, Proposition 3.2]).
Invariants along the recollements of Gorenstein derived categories
2024, Communications in Algebra