Let T be a Krull–Schmidt, Hom-finite triangulated category with suspension functor [1]. Let R
be a basic rigid object, Γ the endomorphism algebra of R, and pr (R)⊆ T the subcategory 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 …

Abstract We consider a Krull–Schmidt, Hom-finite, 2-Calabi–Yau triangulated category with
a basic rigid object T, and show a bijection between the set of isomorphism classes of basic …

In this paper, we study a close relationship between relative cluster tilting theory in
extriangulated categories and τ-tilting theory in module categories. Our main results show …

This note compares τ-tilting modules and maximal rigid objects in the context of 2-Calabi-
Yau triangulated categories. Let 𝓒 be a 2-Calabi-Yau triangulated category with suspension …

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 …

Let $\mathcal {A} $ be a Hom-finite abelian category with enough projectives. In this note,
we show that any covariantly finite $\tau $-rigid subcategory is contained in a support $\tau …

Abstract If (A, B) and (A′, B′) are co-t-structures of a triangulated category, then (A′, B′)
is called intermediate if A⊆ A′⊆ Σ A. Our main results show that intermediate co-t …

We study IE-closed subcategories of a module category, subcategories which are closed
under taking Images and Extensions. We investigate the relation between IE-closed …

We show that a right triangulated category is best behaved when its shift satisfies conditions
making it what we call a right semi-equivalence. We consider right triangulated categories …