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 …

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 …

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 …

Let B be an extriangulated category with enough projectives and enough injectives. Let C be
a fully rigid subcategory of B which admits a twin cotorsion pair ((C, K),(K, D)). The quotient …

For a triangulated category C with a cluster tilting subcategory T which contains infinitely
many indecomposable objects, the notion of weak T [1]-cluster tilting subcategories of C is …

Let $\mathcal C $ be a Krull-Schmidt triangulated category with shift functor $[1] $ and
$\mathcal R $ be a rigid subcategory of $\mathcal C $. We are concerned with the mutation …

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 (C, E, s) be an extriangulated category. We show that certain quotient categories of
extriangulated categories are equivalent to module categories by some restriction of functor …

In this paper, the authors introduce a new definition of∞-tilting (resp. cotilting) subcategories
with infinite projective dimensions (resp. injective dimensions) in an extriangulated category …

Let $\mathscr {C} $ be an extriangulated category with enough projectives and injectives.
We give a new definition of tilting subcategories of $\mathscr {C} $ and prove it coincides …