arXiv subjects

Dandan Sun

Publications and source records attributed to Dandan Sun.

4 recordsLinked to original sources

arXiv2026

Chains of model structures arising from cotorsion pairs on extriangulated categories

The main aim of this paper is to study chains of model structures arising from cotorsion pairs in extriangulated categories. Starting with a hereditary Hovey triple, we construct further hereditary Hovey triples whose homotopy categories are equivalent under suitable completeness assumptions, thereby refining results due to El Maaouy and Shao-Wang-Zhang. As an application, we consider objects of finite Gorenstein injective dimension with respect to a proper class of $\mathbb{E}$-triangles. Under mild set-theoretic assumptions, we obtain a chain of model structures whose homotopy categories are all triangulated equivalent to a common stable category. This recovers known results for Gorenstein injective modules and yields new examples in the derived category of a ring when the proper class is given by cohomological ghost triangles.

math.RT↗

arXiv2025

Ideal approximation theory in Frobenius categories

Let $\mathcal{A}$ be a Frobenius category and $\omega$ the full subcategory consisting of projective objects. The relations between special precovering (resp., precovering) ideals in $\mathcal{A}$ and special precovering (resp., preenveloping) ideals in the stable category $\mathcal{A}/\omega$ are explored. In combination with a result due to Breaz and Modoi, we conclude that every precovering or preenveloping ideal $\mathcal{I}$ in $\mathcal{A}$ with $1_{X}\in{\mathcal{I}}$ for any $X\in{\omega}$ is special. As a consequence, it is proved that an ideal cotorsion pair $(\mathcal{I},\mathcal{J})$ in $\mathcal{A}$ is complete if and only if $\mathcal{I}$ is precovering if and only if $\mathcal{J}$ is preenveloping. This leads to an ideal version of the Bongartz-Eklof-Trlifaj Lemma in $\mathcal{A}/\omega$, which states that an ideal cotorsion pair in $\mathcal{A}/\omega$ generated by a set of morphisms is complete. As another consequence, we provide some partial answers to the question about the completeness of cotorsion pairs posed by Fu, Guil Asensio, Herzog and Torrecillas.

math.CT↗

arXiv2024

Cotorsion pairs and Enochs Conjecture for object ideals

Let $\mathcal{I}$ and $\mathcal{J}$ be object ideals in an exact category $(\mathcal{A}; \mathcal{E})$. It is proved that $(\mathcal{I},\mathcal{J})$ is a perfect ideal cotorsion pair if and only if $({\rm Ob}(\mathcal{I}),{\rm Ob}(\mathcal{J}))$ is a perfect cotorsion pair, where ${\rm Ob}(\mathcal{I})$ and ${\rm Ob}(\mathcal{J})$ is the objects of $\mathcal{I}$ and $\mathcal{J}$, respectively. If in addition $(\mathcal{A}; \mathcal{E})$ has enough projective objects and injective objects, and $\mathcal{J}$ is enveloping, then $(\mathcal{I},\mathcal{J})$ is a complete ideal cotorsion pair if and only if $({\rm Ob}(\mathcal{I}),{\rm Ob}(\mathcal{J}))$ is a complete cotorsion pair. This gives a partial answer to the question posed by Fu, Guil Asensio, Herzog and Torrecillas. Moreover, for any object ideal $\mathcal{I}$ in the category of left $R$-modules, it is proved that $\mathcal{I}$ satisfies Enochs Conjecture if and only if ${\rm Ob}(\mathcal{I})$ satisfies Enochs Conjecture. Applications are given to projective morphisms and ideal cotorsion pairs $(\mathcal{I},\mathcal{J})$ of object ideals under certain conditions.

math.CT↗

arXiv2021

Recollements induced by left Frobenius pairs

Given a right exact functor from an abelian category into another abelian category, there is an associated abelian category called the comma category of the functor. In this paper, we characterize when left Frobenius pairs (resp. strong left Frobenius pairs) in abelian categories can induce left Frobenius pairs (resp. strong left Frobenius pairs) in their comma categories. This leads to the construction of recollements of right triangulated categories (resp. triangulated categories) from the stable categories of left Frobenius pairs (resp. strong left Frobenius pairs). Applications are given to complete hereditary cotorsion pairs and Gorenstein projective objects.

math.RA↗