Lifting recollements of abelian categories and model structures

Georgios Dalezios; Chrysostomos Psaroudakis

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arXiv · 2203.00496

Lifting recollements of abelian categories and model structures

Georgios Dalezios·Chrysostomos Psaroudakis

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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.

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BibTeX RIS

Georgios Dalezios, Chrysostomos Psaroudakis. 2022-03-01. Lifting recollements of abelian categories and model structures. https://arxiv.org/abs/2203.00496

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