arXiv subjects

Yixia Zhang

Publications and source records attributed to Yixia Zhang.

2 recordsLinked to original sources

arXiv2026

Ideal $n$-cotorsion pairs in Frobenius extriangulated categories

Motivated by the correspondence between ideal cotorsion pairs in Frobenius exact categories and those in their stable categories, we introduce the notion of an ideal $n$-cotorsion pair in an extriangulated category. We study the relationship between ideal $n$-cotorsion pairs in a Frobenius extriangulated category $\mathcal C$ and those in its stable category $\underline{\mathcal C}=\mathcal C/ω$. Our main result shows that $(\mathcal I,\mathcal J)$ is an ideal $n$-cotorsion pair in $\mathcal C$ if and only if $(\mathcal I/ω,\mathcal J/ω)$ is an ideal $n$-cotorsion pair in $\underline{\mathcal C}$. This provides a bridge between higher ideal approximation theory in Frobenius extriangulated categories and its counterpart in their stable categories. Additionally, in Krull--Schmidt exact categories, we establish a bijective correspondence between complete cotorsion pairs and complete ideal cotorsion pairs, answering a question of Fu, Guil Asensio, Herzog and Torrecillas.

math.RT↗

arXiv2025

Triangulated categories arising from n-fold matrix factorizations

Let $\mathcal{A}$ be an additive category and let $T\colon \mathcal{A}\rightarrow \mathcal{A}$ be an additive functor equipped with a natural transformation $ω\colon \mathrm{Id}_{\mathcal{A}}\rightarrow T$. We prove that the homotopy category of $n$-fold matrix factorizations of $ω$, denoted ${\rm HFact}_{n}(\mathcal{A},T,ω)$, admits a natural structure of a right triangulated category. In particular, when $T$ is an automorphism, the homotopy category ${\rm HFact}_{n}(\mathcal{A},T,ω)$ becomes triangulated. Furthermore, if $\mathcal{A}$ is a Frobenius exact category and $T$ is an autoequivalence, we obtain that the category ${\rm Fact}_{n}(\mathcal{A},T,ω)$ of $n$-fold $(\mathcal{A},T)$-factorizations of $ω$ is a Frobenius exact category. Consequently, the stable category of the Frobenius exact category ${\rm Fact}_{n}(\mathcal{A},T,ω)$ is a triangulated category.

math.RT↗