Model structure arising from one hereditary cotorsion pair on extriangulated categories

2024/06/20 by Hu, Jiangsheng, Zhang, Dongdong, Zhou, Panyue · 1 citation
#Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2406.14031

Abstract

Let C be a weakly idempotent complete extriangulated category. In contrast with the Hovey correspondence of admissible model structures on weakly idempotent complete exact categories from two complete cotorsion pairs, we give a construction of model structures on C from only one complete cotorsion pair. Our main result not only generalizes the work by Beligiannis-Reiten and Cui-Lu-Zhang, but also provides methods to construct model structures from silting objects of C and co-t-structures in triangulated categories.

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• Induced complete hereditary cotorsion pairs in D(R) with respect to Cartan-Eilenberg exact sequences

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