In particular, we will show how the tilting theory in exact categories built this way, coincides with tilting objects in extriangulated categories introduced recently. We will review Bazzoni's tilting characterization, the relative homological dimensions on the induced tilting classes and parametrise ...
We develop theory of (possibly large) cotilting objects of injective dimension at most one in general Grothendieck categories. We show that such cotilting objects are always pure-injective and that they characterize the situation where the Grothendieck category is tilted using a torsion pair to anot...
In this article we introduce the notion of [Formula: see text]-tilting objects in an extriangulated category, where [Formula: see text] is a proper class of [Formula: see text]-triangles. Our results extend the relative tilting theory in extriangulated categories....
If moreover the exact category has higher kernels, then its image coincides with the category naturally associated with a cotilting subcategory up to summands. We apply these results to the representation theory of artin algebras. In particular, we show that the ideal quotient of a module ...
FUNCTOR theoryPROJECTIVE modules (AlgebraIn this article we further study the full subcategories of the category of finitely generated modules over an Artin algebra introduced in Platzeck and Pratti (2000), consisting of the modules having an add M resolution of length i, which remains exact under...
Theory 4(2), 155–170 (2001) Angeleri Hügel, L., Hrbek, M.: Silting modules over commutative rings. Int. Math. Res. Not. IMRN 2017(13), 4131–4151 (2017) MathSciNet Google Scholar Angeleri Hügel, L., Hrbek, M.: Parametrizing torsion pairs in derived categories. Represent. Theory...
In Sect. 6, we describe filtrations of the objects in the categories T ⊥ ⊆ -mod and ⊥( DT ) ⊆ -mod, finding parallels with the theory of quasi-hereditary algebras. As is the case for the latter algebras, any truncated path algebra is standardly stratified (in the weak sense ...
-cluster tilting subcategories are an ideal setting for higher dimensional Auslander–Reiten theory. We give a complete classification of-cluster tilting subcategories of module categories of Nakayama algebras given by quivers with relations. In particular, we show that there are three kinds of Nakayama...
The Nakayama conjecture states that an algebra of infinite dominant dimension should be self-injective. Motivated by understanding this conjecture in the context of derived categories, we study dominant dimensions of algebras under derived equivalences induced by tilting modules, specifically, the infinity...
we show that tilting (cotilting) subcategories defined here unify many previous works about tilting theory in module categories of Artin algebras and abelian categories admitting a cotorsion triples; we also show that the results work for triangulated categories with a proper class of triangles introdu...