Ladders of recollements of abelian categories
Nan Gao, Steffen Koenig, Chrysostomos Psaroudakis

TL;DR
This paper introduces ladders of recollements in abelian categories, enabling the construction of triangulated category recollements, tilting of abelian recollements, and preservation of properties like Gorenstein conditions.
Contribution
It develops the theory of ladders of recollements, providing new methods to relate abelian and triangulated categories and to preserve important properties.
Findings
Ladders of a certain height construct triangulated recollements from abelian ones.
Ladders facilitate tilting of abelian recollements.
Ladders ensure preservation of Gorenstein properties in functors.
Abstract
Ladders of recollements of abelian categories are introduced, and used to address three general problems. Ladders of a certain height allow to construct recollements of triangulated categories, involving derived categories and singularity categories, from abelian ones. Ladders also allow to tilt abelian recollements, and ladders guarantee that properties like Gorenstein projective or injective are preserved by some functors in abelian recollements. Breaking symmetry is crucial in developing this theory.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Advanced Topics in Algebra
