arXiv subjects

Yajun Ma

Publications and source records attributed to Yajun Ma.

15 recordsLinked to original sources

arXiv2026

Model structures on the category of Q-shaped modules

We develop a method for constructing abelian model structures on the category Q,AMod of Q-shaped modules from cotorsion pairs in AMod, where Q is a small preadditive category satisfying certain conditions and AMod denotes the category of left A-modules for any ring A. More precisely, we construct two cotorsion pairs in Q,AMod from a given cotorsion pair in AMod. This leads to a construction of projective model structures on Q,AMod under the condition that Q has no cycles. We further apply this method to the category Dif(A) of differential left A-modules, viewed as a category of Q-shaped modules for a suitable choice of Q. In this case, the induced cotorsion pairs are shown to be compatible, thereby giving rise to abelian model structures on Dif(A).

math.RT↗

arXiv2026

Flat models for Q-shaped derived categories via PGF objects

We develop a unified approach, based on projectively coresolved Gorenstein flat (PGF) objects, for constructing flat model structures on diagram categories. Specifically, we show that PGF objects in such categories are fully determined by their objectwise components, which in turn enables us to establish hereditary abelian model structures whose trivial cofibrant objects are precisely the flat objects. As an application, we reobtain flat model structures on $Q$-shaped derived categories, thereby providing a common framework that subsumes classical constructions for chain complexes. Moreover, we obtain an explicit description of the cofibrant objects in these models.

math.RT↗

arXiv2026

Igusa-Todorov properties of recollements of abelian categories

In this paper, we investigate the behavior of Igusa-Todorov properties under recollements of abelian categories. In particular, we study how the Igusa-Todorov distances of the categories involved in a recollement are related. Applications are given to Artin algebras, especially to Morita context rings.

math.RT↗

arXiv2025

Homological invariant properties under cleft extensions

We study the behavior of the Gorenstein weak global dimension under a cleft extension of rings; we prove that under some mild conditons the finiteness of the Gorenstein weak global dimension is invariant. Moreover, we compare the relative singularity categories with respect to flat-cotorsion modules under a cleft extension of rings. Some applications to θ-extensions and Morita context rings are given.

math.CT↗

arXiv2024

Three homological invariants under cleft extensions

In this paper, we investigate the behavior of Igusa-Todorov distances, extension and Rouquier dimensions under cleft extensions of abelian categories. We apply our results to Morita context rings, trivial extension rings, tensor rings and arrow removals.

math.CT↗

arXiv2024

Admissible weak factorization systems on extriangulated categories

Extriangulated categories, introduced by Nakaoka and Palu, serve as a simultaneous generalization of exact and triangulated categories. In this paper, we first introduce the concept of admissible weak factorization systems and establish a bijection between cotorsion pairs and admissible weak factorization systems in extriangulated categories. Consequently, we give the equivalences between hereditary cotorsion pairs and compatible cotorsion pairs via admissible weak factorization systems under certain conditions in extriangulated categories, thereby generalizing a result by Di, Li, and Liang.

math.CT↗

arXiv2023

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↗

arXiv2022

Flat model structures and Gorenstein objects in functor categories

We construct a flat model structure on the category $_{\mathcal{Q},R}{\mathsf{Mod}}$ of additive functors from a small preadditive category $\mathcal{Q}$ satisfying certain conditions to the module category $_{R}{\mathsf{Mod}}$ over an associative ring $R$, whose homotopy category is the $\mathcal{Q}$-shaped derived category introduced by Holm and Jorgensen. Moreover, we prove that for an arbitrary associative ring $R$, an object in $_{\mathcal{Q},R}{\mathsf{Mod}}$ is Gorenstein projective (resp., Gorenstein injective, Gorenstein flat, projective coresolving Gorenstein flat) if and only if so is its value on each object of $\mathcal{Q}$, and hence improve a result by Dell'Ambrogio, Stevenson and \v{S}\v{t}ov\'{\i}\v{c}ek.

math.RT↗

arXiv2022

MDC Enhanced IoT Networks: Network Modeling and Performance Analysis

As a promising architecture, Mobile Data Collector (MDC) enhanced Internet of Things (IoT) exhibits broad prospects in efficient data collection and data aggregation especially for sparse deployment scenarios. Combining the tools from queueing theory and stochastic geometry, we propose an analytical framework to study the network performance of an MDC enhanced IoT network, in terms of coverage probability, end-to-end delay and energy consumption. We derive the closed-form expressions for average contact and inter-contact time between a sensor and its associated MDC. By modeling the data collection system between a sensor and its associated MDCs as an M/G/1 queue system with vacations and general limited (G-limited) service, we first derive the queueing delay at the tagged sensor, and further obtain the end-to-end delay. The proposed analytical framework enables us to quantify the effect on network performance of key system parameters, such as MDC velocity, packet arrival rate, densities of sensors and MDCs, and contact radius. This study reveals that the MDC velocity has little impact on the coverage probability, and provides guidelines to minimize the end-to-end delay by optimizing the density and contact radius of sensors, and the velocity and density of MDCs.

cs.NI↗

arXiv2022

How to construct Gorenstein projective modules relative to complete duality pairs over Morita rings

Let $Δ=\left(\begin{smallmatrix} A & {_AN_B}\\ {_BM_A} & B \\\end{smallmatrix}\right)$ be a Morita ring with $M\otimes_{A}N=0=N\otimes_{B}M$.We first study how to construct (complete) duality pairs of $Δ$-modules using (complete) duality pairs of $A$-modules and $B$-modules, generalizing the result of Mao (Comm. Algebra, 2020, 12: 5296--5310) about the duality pairs over a triangular matrix ring. Moreover, we construct Gorenstein projective modules relative to complete duality pairs of $Δ$-modules. Finally, we give an application to Ding projective modules.

math.RA↗

arXiv2021

A new characterization of silting subcategories in the stable category of a Frobenius extriangulated category

We give a new characterization of silting subcategories in the stable category of a Frobenius extriangulated category, generalizing the result of Di et al. (J. Algebra 525 (2019) 42-63) about the Auslander-Reiten type correspondence for silting subcategories over triangulated categories. More specifically, for any Frobenius extriangulated category $\mathcal{C}$, we establish a bijective correspondence between silting subcategories of the stable category $\underline{\mathcal{C}}$ and certain covariantly finite subcategories of $\mathcal{C}$. As a consequence, a characterization of silting subcategories in the stable category of a Frobenius exact category is given. This result is applied to homotopy categories over abelian categories with enough projectives, derived categories over Grothendieck categories with enough projectives as well as to the stable category of Gorenstein projective modules over a ring $R$.

math.RA↗

arXiv2021

Higher Auslander's defect and classifying substructures of n-exangulated categories

Herschend-Liu-Nakaoka introduced the notion of $n$-exangulated categories. It is not only a higher dimensional analogue of extriangulated categories defined by Nakaoka-Palu, but also gives a simultaneous generalization of $n$-exact categories and $(n+2)$-angulated categories. In this article, we give an $n$-exangulated version of Auslander's defect and Auslander-Reiten duality formula. Moreover, we also give a classification of substructures (=closed subbifunctors) of a given skeletally small $n$-exangulated category by using the category of defects.

math.RT↗

arXiv2021

A new method to construct model structures from left Frobenius pairs in extriangulated categories

Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous generalization of exact categories and triangulated categories. In this paper, we first introduce the concept of left Frobenius pairs on an extriangulated category C, and then establish a bijective correspondence between Frobenius pairs and certain cotorsion pairs in C. As an application, some new admissible model structures are established from left Frobenius pairs under certain conditions, which generalizes a result of Hu et al. (J. Algebra 551 (2020) 23-60).

math.CT↗

arXiv2021

Quantitative Parametric Mapping of Tissues Properties from Standard Magnetic Resonance Imaging Enabled by Deep Learning

Magnetic resonance imaging (MRI) offers superior soft tissue contrast and is widely used in biomedicine. However, conventional MRI is not quantitative, which presents a bottleneck in image analysis and digital healthcare. Typically, additional scans are required to disentangle the effect of multiple parameters of MR and extract quantitative tissue properties. Here we investigate a data-driven strategy Q^2 MRI (Qualitative and Quantitative MRI) to derive quantitative parametric maps from standard MR images without additional data acquisition. By taking advantage of the interdependency between various MRI parametric maps buried in training data, the proposed deep learning strategy enables accurate prediction of tissue relaxation properties as well as other biophysical and biochemical characteristics from a single or a few images with conventional T_1/T_2 weighting. Superior performance has been achieved in quantitative MR imaging of the knee and liver. Q^2 MRI promises to provide a powerful tool for a variety of biomedical applications and facilitate the next generation of digital medicine.

physics.med-ph↗

arXiv2020

Auslander-Buchweitz Approximation Theory for Extriangulated Categories

Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous generalization of exact categories and triangulated categories. In this paper, we introduce and develop an analogous theory of Auslander-Buchweitz approximations for extriangulated categories. We establish the existence of precovers pand preenvelopesq and obtain characterizations of relative homological dimensions, which are based on certain subcategories under finiteness of resolutions. Finally, we give a description of cotorsion pairs on extriangulated categories under some conditions, and provide a characterization of silting subcategories on stable categories. Keywords: Extriangulated category; Homological dimension; Cogenerator; Cotorsion pair.

math.CT↗