Lifting recollements of abelian categories and model structures

2022/03/01 by Γεώργιος Δαλέζιος, Dalezios, Georgios, Chrysostomos Psaroudakis +1 · 2 citations
Mathematics · #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2203.00496

Abstract

We use Quillen model structures to show a systematic method to lift recollements of hereditary abelian model categories to recollements of their associated homotopy categories. To that end, we use the notion of Quillen adjoint triples and we investigate transfers of abelian model structures along adjoint pairs. Applications include liftings of recollements of module categories to their derived counterpart, liftings to homotopy categories that provide models for stable categories of Gorenstein projective and injective modules and liftings to homotopy categories of n-morphism categories over Iwanaga-Gorenstein rings.

Cited by

• The proper stable module category of a group algebra
• Models for chain homotopy category of relative acyclic complexes

Related

• Gluing and lifting exact model structures for the recollement of exact categories
• Quillen equivalence for chain homotopy categories induced by balanced pairs
• Models for singularity categories
• Hereditary abelian model categegories
• Exact model structures and recollements