2021
DOI: 10.1017/prm.2021.3
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Lifting of recollements and gluing of partial silting sets

Abstract: This paper focuses on recollements and silting theory in triangulated categories. It consists of two main parts. In the first part a criterion for a recollement of triangulated subcategories to lift to a torsion torsion-free triple (TTF triple) of ambient triangulated categories with coproducts is proved. As a consequence, lifting of TTF triples is possible for recollements of stable categories of repetitive algebras or self-injective finite length algebras and recollements of bounded derived categories of sep… Show more

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Cited by 5 publications
(3 citation statements)
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“…Recall that precovers (respectively preenvelopes) are the same as right (respectively left) approximations. The following is a consequence of [15,Lemma 5.3], but we provide a proof for the benefit of the reader.…”
Section: The Gap Theoremmentioning
confidence: 96%
“…Recall that precovers (respectively preenvelopes) are the same as right (respectively left) approximations. The following is a consequence of [15,Lemma 5.3], but we provide a proof for the benefit of the reader.…”
Section: The Gap Theoremmentioning
confidence: 96%
“…We say that D is compactly generated when it has a generating set of compact objects. Denote by D c the subcategory of compact objects of D. The lemma we give below is implicit in [19,Theorem 3.3…”
Section: Lifting Of Ttf Triplesmentioning
confidence: 99%
“…To any recollement one canonically associates a TTF triple. Recently, M.Saorín and A.Zvonareva [19] gave a criterion for a recollement of triangulated subcategories to lift to a torsion torsionfree triple (TTF triple, simply) of ambient triangulated categories with coproducts. L.Angeleri Hügel, S.Koenig, Q.H.Liu and D.Yang [2] introduced and used ladders of recollements as the main tool to clarify the lifting and restriction of the different level of derived categories.…”
Section: Introductionmentioning
confidence: 99%