Related papers: The tilting-cotilting correspondence

An important result in tilting theory states that a class of modules over a ring is a tilting class if and only if it is the Ext-orthogonal class to a set of compact modules of bounded projective dimension. Moreover, cotilting classes are…

For any good tilting module $T$ over a ring $A$, there exists an $n$-symmetric subcategory $\mathscr{E}$ of a module category such that the derived category of the endomorphism ring of $T$ is a recollement of the derived categories of…

We construct an exact tensor functor from the category $\mathcal{A}$ of finite-dimensional graded modules over the quiver Hecke algebra of type $A_\infty$ to the category $\mathscr C_{B^{(1)}_n}$ of finite-dimensional integrable modules…

We consider an arbitrary Abelian category $\mathcal{A}$ and a subcategory $\mathcal{T}$ closed under extensions and direct summands, and characterize those $\mathcal{T}$ that are (semi-)special preenveloping in $\mathcal{A}$; as a…

An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that traditional homological algebra is…

We consider filtrations of objects in an abelian category $\catA$ induced by a tilting object $T$ of homological dimension at most two. We define three disjoint subcategories with no maps between them in one direction, such that each object…

We prove general results about completeness of cotorsion theories and existence of covers and envelopes in locally presentable abelian categories, extending the well-established theory for module categories and Grothendieck categories.…

We introduce the notion of noncompact (partial) silting and (partial) tilting sets and objects in any triangulated category D with arbitrary (set-indexed) coproducts. We show that equivalence classes of partial silting sets are in bijection…

We generalize Brenner and Butler's Theorem as well as Happel's Theorem on the equivalences induced by a finitely generated tilting module over artin algebras, to the case of an infinitely generated tilting module over an arbitrary…

Derived equivalences and t-structures are closely related. We use realisation functors associated to t-structures in triangulated categories to establish a derived Morita theory for abelian categories with a projective generator or an…

We classify all tilting classes over an arbitrary commutative ring via certain sequences of Thomason subsets of the spectrum, generalizing the classification for noetherian commutative rings by…

We define tilting subcategories in arbitrary exact categories to archieve the following. Firstly: Unify existing definitions of tilting subcategories to arbitrary exact categories. Discuss standard results for tilting subcategories:…

Tilting theory in cluster categories of hereditary algebras has been developed in [BMRRT] and [BMR]. These results are generalized to cluster categories of hereditary abelian categories. Furthermore, for any tilting object $T$ in a…

This is the second paper in a series on representations over diagrams of abelian categories. We show that, under certain conditions, a compatible family of abelian model categories indexed by a skeletal small category can be amalgamated…

Let $\mathscr{A}$ be an abelian category having enough projective and injective objects, and let $\mathscr{T}$ be an additive subcategory of $\mathscr{A}$ closed under direct summands. A known assertion is that in a short exact sequence in…

Let $R$ be a ring and Ch($R$) the category of chain complexes of $R$-modules. We put an abelian model structure on Ch($R$) whose homotopy category is equivalent to $K(Proj)$, the homotopy category of all complexes of projectives. However,…

Given an abelian category, we introduce a categorical concept of (strongly) Gorenstein projective (resp., injective) objects, by defining a new special class of objects. Then we study the transfer of these properties when passing to an…

For any graded commutative noetherian ring, where the grading group is abelian and where commutativity is allowed to hold in a quite general sense, we establish an inclusion-preserving bijection between, on the one hand, the twist-closed…

Let $\mathcal{A}$ be an abelian category. For a pair $(\mathcal{X},\mathcal{Y}$ of classes of objects in $\mathcal{A},$ we define the weak and the $(\mathcal{X},\mathcal{Y})$-Gorenstein relative projective objects in $\mathcal{A}$. We point…

For a commutative noetherian ring A, we compare the support of a complex of A-modules with the support of its cohomology. This leads to a classification of all full subcategories of A-modules which are thick (that is, closed under taking…