Tilting categories with applications to stratifying systems.

DOI10.1016/j.jalgebra.2006.01.006zbMath1122.16008OpenAlexW2090222333MaRDI QIDQ852681

Corina Sáenz, Octavio Mendoza

Publication date: 15 November 2006

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2006.01.006

zbMATH Keywords

Artin algebrasGorenstein algebrasfinitistic dimensionstratifying systemsstratified algebrascontravariantly finite subcategoriesfiltration dimensionshomological invariants of algebraslengths of resolutionstilting categories

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Representations of associative Artinian rings (16G10) Homological dimension in associative algebras (16E10)

Related Items (13)

Relative Igusa-Todorov functions and relative homological dimensions ⋮ Frobenius pairs in abelian categories. Frobenius pairs in abelian categories, correspondences with cotorsion pairs, exact model categories, and Auslander-Buchweitz contexts ⋮ Quadratic forms associated to stratifying systems. ⋮ Cut cotorsion pairs ⋮ Relative tilting classes in extriangulated categories ⋮ Auslander-Buchweitz approximation theory for triangulated categories ⋮ \(n\)-term silting complexes in \(\mathsf{K}^b (\mathrm{proj}(\Lambda))\) ⋮ An approach to the finitistic dimension conjecture. ⋮ Homological dimensions in cotorsion pairs. ⋮ Relative Gorenstein objects in abelian categories ⋮ Split-By-Nilpotent Extensions Algebras and Stratifying Systems ⋮ Stratifying systems through \(\tau\)-tilting theory ⋮ Relative global Gorenstein dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Applications of stratifying systems to the finitistic dimension.
• Stratifying systems via relative simple modules.
• Applications of contravariantly finite subcategories
• Finitistic dimension of properly stratified algebras.
• Standardly stratified algebras and tilting
• The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences
• MODULES OF FINITE PROJECTIVE DIMENSION FOR STANDARDLY STRATIFIED ALGEBRAS
• On Good Filtration Dimensions for Standardly Stratified Algebras
• The homological theory of maximal Cohen-Macaulay approximations
• On Standardly Stratified Algebras
• APPLICATIONS OF COTORSION PAIRS
• Stratifying Systems via Relative Projective Modules
• The global dimension of Schur algebras for \(\text{GL}_2\) and \(\text{GL}_3\)

This page was built for publication: Tilting categories with applications to stratifying systems.