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 …
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 …
[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 …
General heart construction on a triangulated category (II): Associated homological functor
N Abe, H Nakaoka - Applied Categorical Structures, 2012 - Springer
In the preceding part (I) of this paper, we showed that for any torsion pair (ie, t-structure
without the shift-closedness) in a triangulated category, there is an associated abelian …
without the shift-closedness) in a triangulated category, there is an associated abelian …
[PDF][PDF] On derived categories and derived functors
S Saneblidze - arXiv preprint arXiv:0710.5065, 2007 - arxiv.org
arXiv:0710.5065v3 [math.AT] 28 Oct 2008 Page 1 arXiv:0710.5065v3 [math.AT] 28 Oct 2008
ON DERIVED CATEGORIES AND DERIVED FUNCTORS SAMSON SANEBLIDZE Abstract …
ON DERIVED CATEGORIES AND DERIVED FUNCTORS SAMSON SANEBLIDZE Abstract …
A double-dimensional approach to formal category theory
SR Koudenburg - arXiv preprint arXiv:1511.04070, 2015 - arxiv.org
Whereas formal category theory is classically considered within a $2 $-category, in this
paper a double-dimensional approach is taken. More precisely we develop such theory …
paper a double-dimensional approach is taken. More precisely we develop such theory …
Auslander-Buchweitz context and co-t-structures
O Mendoza, EC Sáenz, V Santiago… - arXiv preprint arXiv …, 2010 - arxiv.org
We show that the relative Auslander-Buchweitz context on a triangulated category $\T $
coincides with the notion of co-$ t $-structure on certain triangulated subcategory of $\T …
coincides with the notion of co-$ t $-structure on certain triangulated subcategory of $\T …
The tilting–cotilting correspondence
L Positselski, J Šťovíček - International Mathematics Research …, 2021 - academic.oup.com
To a big-tilting object in a complete, cocomplete abelian category with an injective
cogenerator we assign a big-cotilting object in a complete, cocomplete abelian category with …
cogenerator we assign a big-cotilting object in a complete, cocomplete abelian category with …
Auslander–Buchweitz Context and Co-t-structures
O Mendoza Hernández, EC Sáenz Valadez… - Applied Categorical …, 2013 - Springer
We show that the relative Auslander–Buchweitz context on a triangulated category T
coincides with the notion of co-t-structure on certain triangulated subcategory of T (see …
coincides with the notion of co-t-structure on certain triangulated subcategory of T (see …
Derived categories for Grothendieck categories of enriched functors
G Garkusha, D Jones - Contemp. Math, 2019 - books.google.com
The derived category D [C, V] of the Grothendieck category of enriched functors [C, V], where
V is a closed symmetric monoidal Grothendieck category and C is a small V-category, is …
V is a closed symmetric monoidal Grothendieck category and C is a small V-category, is …