Abelian model structures on comma categories

Guoliang Tang

doi:10.3842/umzh.v76i3.7289

Guoliang Tang School of Mathematics and Statistics, Kashi University, China

DOI: https://doi.org/10.3842/umzh.v76i3.7289

Keywords: Abelian model structures; Comma categories; Triangular matrix rings.

Abstract

UDC 512.64

Let $\mathsf{A}$ and $\mathsf{B}$ be bicomplete Abelian categories, which both have enough projectives and injectives and let $T\colon\mathsf{A}\rightarrow\mathsf{B}$ be a right exact functor. Under some mild conditions, we show that hereditary Abelian model structures on $\mathsf{A}$ and $\mathsf{B}$ can be amalgamated into a global hereditary Abelian model structure on the comma category $(T\downarrow\mathsf{B})$. As an application of this result, we give an explicit description of a subcategory that consists of all trivial objects of the Gorenstein flat model structure on the category of modules over a triangular matrix ring.

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