In the preceding part (I) of this paper, we showed that for any torsion pair (ie, t-structure
without the shift-closedness) in a triangulated category, there is an associated abelian …

Let C be a triangulated category with shift functor [1] and R a rigid subcategory of C. We
introduce the notions of two-term R [1]-rigid subcategories, two-term (weak) R [1]-cluster …

Full article: Lifting to Cluster-Tilting Objects in 2-Calabi–Yau Triangulated Categories Skip
to Main Content Taylor and Francis Online homepage Taylor and Francis Online homepage …

For a Calabi-Yau triangulated category $\mathcal {C} $ of Calabi-Yau dimension $ d $ with a
$ d-$ cluster tilting subcategory $\mathcal {T} $, it is proved that the decomposition of …

Let be an extriangulated category with enough projectives P \mathcalP and enough
injectives I \mathcalI, and let be a contravariantly finite rigid subcategory of which contains P …

For a triangulated category TT, if CC is a cluster-tilting subcategory of TT, then the factor
category T/CT/C is an abelian category. Under certain conditions, the converse also holds …

Extriangulated category was introduced by H. Nakaoka and Y. Palu to give a unification of
properties in exact categories and triangulated categories. A notion of tilting (resp., cotilting) …

In this paper, we prove that if a triangulated category D admits a recollement relative to
triangulated categories D'and D'', then the abelian category D/T admits a recollement …

Let $ k $ be a field, and let ${\mathcal {C}} $ be a $ k $-linear, Hom-finite triangulated
category with split idempotents. In this paper, we show that under suitable circumstances …

Based on Beligiannis's theory in [Beligiannis, A.(2000). Relative homological algebra and
purity in triangulated categories. J. Algebra 227 (1): 268–361], we introduce and study E …