The Monomorphism Category of Gorenstein Projective Modules and Comparison with the Category of Matrix Factorizations

Abstract

Let (S,n) be a commutative noetherian local ring and let ω∈n be non-zero divisor. This paper is concerned with the category of monomorphisms between finitely generated Gorenstein projective S-modules, such that their cokernels are annihilated by ω. We will observe that this category, which will be denoted by Mon(ω,G), is an exact category in the sense of Quillen. More generally, it is proved that Mon(ω,G) is a Frobenius category. Surprisingly, it is shown that not only the category of matrix factorizations embeds into Mon(ω,G), but also its stable category as well as the singularity category of the factor ring R=S/(ω), can be realized as triangulated subcategories of the stable category Mon̲(ω,G). © The Author(s) under exclusive licence to Iranian Mathematical Society 2025.