25 citations · 102 across the 10 of their papers we have counts for
17 papers
Tilting preenvelopes and cotilting precovers in general Abelian categories
Carlos E. Parra, Manuel Saorín, Simone Virili
We consider an arbitrary Abelian category and a subcategory closed under extensions and direct summands, and characterize those that are (…
-Structures with Grothendieck hearts via functor categories
Manuel Saorín, Jan Šťovíček
We study when the heart of a t-structure in a triangulated category with coproducts is AB5 or a Grothendieck category. If satisfies Brown representabili…
The HRS tilting process and Grothendieck hearts of t-structures
Carlos E. Parra, Manuel Saorín
In this paper we revisit the problem of determining when the heart of a t-structure is a Grothendieck category, with special attention to the case of the Happel-Reiten-Smalø (HSR)…
Locally finitely presented and coherent hearts
Carlos E. Parra, Manuel Saorín, Simone Virili
Starting with a Grothendieck category and a torsion pair in , we study the local finite presentability and local co…
Torsion pairs in categories of modules over a preadditive category
Manuel Saorín, Carlos Parra, Simone Virili
It is a result of Gabriel that hereditary torsion pairs in categories of modules are in bijection with certain filters of ideals of the base ring, called Gabriel filters or Gabriel…
Degenerating in Triangulated Categories
Manuel Saorín, Alexander Zimmermann
In previous work, based on work of Zwara and Yoshino, we defined and studied degenerations of objects in triangulated categories analogous to degeneration of modules. In triangulat…
Lifting of recollements and gluing of partial silting sets
Manuel Saorín, Alexandra Zvonareva
This paper focuses on recollements and silting theory in triangulated categories. It consists of two main parts. In the first part a criterion for a recollement of triangulated sub…
-Structures on stable derivators and Grothendieck hearts
Manuel Saorín, Jan Šťovíček, Simone Virili
We prove that given any strong, stable derivator and a -structure on its base triangulated category , the -structure canonically lifts to all the (coherent) diagram c…
Contractibility of the stability manifold for silting-discrete algebras
David Pauksztello, Manuel Saorín, Alexandra Zvonareva
We show that any bounded t-structure in the bounded derived category of a silting-discrete algebra is algebraic, i.e. has a length heart with finitely many simple objects. As a cor…
Dg algebras with enough idempotents, their dg modules and their derived categories
Manuel Saorín
We develop the theory dg algebras with enough idempotents and their dg modules and show their equivalence with that of small dg categories and their dg modules. We introduce the co…
On locally coherent hearts
Manuel Saorín
We show that, under particular conditions, if a t-structure in the unbounded derived category of a locally coherent Grothendieck category restricts to the bounded derived category…
Derived equivalences induced by nonclassical tilting objects
Luisa Fiorot, Francesco Mattiello, Manuel Saorín
Suppose that is an abelian category whose derived category has sets and arbitrary (small) coproducts, let be a (not necessarily c…
Addendum to 'Direct limits in the heart of a t-structure: The case of a torsion pair'
Carlos E. Parra, Manuel Saorín
Let be a Grothendieck category, let be a torsion pair in and let $(\mathcal{U}_\mathbf{t},\mathcal{W}_\mathbf{t})…
Hearts of t-structures in the derived category of a commutative Noetherian ring
Carlos E. Parra, Manuel Saorín
Let be a commutative Noetherian ring and let be its (unbounded) derived category. We show that all compactly generated t-structures in associate…
Direct sums of representations as modules over their endomorphism rings
Birge Huisgen-Zimmermann, Manuel Saorín
This paper is devoted to the study of the endo-structure of infinite direct sums of indecomposable modules over a ring . It is centered on the fo…
On hearts which are module categories
Carlos E. Parra, Manuel Saorín
Given a torsion pair in a module category -Mod we give necessary and sufficient conditions for the associated Happel-Reiten-Smalø$\text…
Direct limits in the heart of a t-structure: the case of a torsion pair
Carlos E. Parra, Manuel Saorín
We study the behavior of direct limits in the heart of a t-structure. We prove that, for any compactly generated t-structure in a triangulated category with exact coproducts, count…