[HTML][HTML] t-Structures on stable derivators and Grothendieck hearts
We prove that, given any strong and stable derivator and a t-structure in its base triangulated
category D, the t-structure canonically lifts to all the (coherent) diagram categories and each …
category D, the t-structure canonically lifts to all the (coherent) diagram categories and each …
Purity in compactly generated derivators and t-structures with Grothendieck hearts
R Laking - Mathematische Zeitschrift, 2020 - Springer
We study t-structures with Grothendieck hearts on compactly generated triangulated
categories TT that are underlying categories of strong and stable derivators. This setting …
categories TT that are underlying categories of strong and stable derivators. This setting …
t-Structures with Grothendieck hearts via functor categories
M Saorín, J Št'ovíček - Selecta Mathematica, 2023 - Springer
We study when the heart of at-structure in a triangulated category D with coproducts is AB5
or a Grothendieck category. If D satisfies Brown representability, at-structure has an AB5 …
or a Grothendieck category. If D satisfies Brown representability, at-structure has an AB5 …
Hearts and towers in stable -categories
D Fiorenza, F Loregian, GL Marchetti - Journal of Homotopy and Related …, 2019 - Springer
We exploit the equivalence between t-structures and normal torsion theories on a stable
∞∞-category to show how a few classical topics in the theory of triangulated categories, ie …
∞∞-category to show how a few classical topics in the theory of triangulated categories, ie …
Co-t-structures: the first decade
P Jørgensen - Surveys in representation theory of algebras, 2018 - books.google.com
Co-t-structures were introduced about ten years ago as a type of mirror image of t-structures.
Like t-structures, they permit us to divide an object in a triangulated category T into a “left …
Like t-structures, they permit us to divide an object in a triangulated category T into a “left …
[HTML][HTML] Averaging t-structures and extension closure of aisles
N Broomhead, D Pauksztello, D Ploog - Journal of Algebra, 2013 - Elsevier
We ask when a finite set of t-structures in a triangulated category can be 'averaged'into one t-
structure or, equivalently, when the extension closure of a finite set of aisles is again an …
structure or, equivalently, when the extension closure of a finite set of aisles is again an …
Characterising the bounded derived category of an hereditary abelian category
A Hubery - arXiv preprint arXiv:1612.06674, 2016 - arxiv.org
We show that if a (not necessarily algebraic) triangulated category T contains an admissible
hereditary abelian subcategory H, then we can lift the inclusion of H into T to a fully faithful …
hereditary abelian subcategory H, then we can lift the inclusion of H into T to a fully faithful …
Morita theory for stable derivators
S Virili - arXiv preprint arXiv:1807.01505, 2018 - arxiv.org
We give a general construction of realization functors for $ t $-structures on the base of a
strong stable derivator. In particular, given such a derivator $\mathbb D $, a $ t $-structure …
strong stable derivator. In particular, given such a derivator $\mathbb D $, a $ t $-structure …
Factorization systems on (stable) derivators
F Loregian, S Virili - arXiv preprint arXiv:1705.08565, 2017 - arxiv.org
We define triangulated factorization systems on triangulated categories, and prove that a
suitable subclass thereof (the normal triangulated torsion theories) corresponds bijectively to …
suitable subclass thereof (the normal triangulated torsion theories) corresponds bijectively to …
[HTML][HTML] Direct limits in the heart of a t-structure: the case of a torsion pair
CE Parra, M Saorín - Journal of pure and applied algebra, 2015 - Elsevier
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 coproducts, countable direct …
compactly generated t-structure in a triangulated category with coproducts, countable direct …