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Xiaohu Chen

Publications and source records attributed to Xiaohu Chen.

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Bounded $t$-structures on the category of strongly bounded objects

Strongly bounded objects in a weakly approximable triangulated category are known to relate closely to global dimension and to play a significant role in the uniqueness problem for triangulated enhancements. In this paper, we investigate when the full subcategory of strongly bounded objects admits a bounded $t$-structure. Our main result, under a finiteness condition termed the finite strong finitistic dimension, states that this happens exactly when the subcategory agrees with the full subcategory of bounded objects in the ambient triangulated category. In that case, the bounded $t$-structure is unique up to equivalence; even more, the uniqueness holds unconditionally on the full subcategory of bounded objects.

math.RT

Triangulated categories with a compact silting object, Brown-Comenetz duality and Brown representability theorems

The paper develops a Brown--Comenetz dual framework for Neeman's representability theorems for triangulated categories with a single compact generator (Invent. math., 244:531-616, 2026). Starting from a locally Hom-finite approximable triangulated category, we use the Brown--Comenetz duals of compact objects to construct a triangulated subcategory $\E$, which plays the role of an injective-side analogue of the compact subcategory $\T^c$. We introduce the intrinsic subcategory $\T_c^+$, dual to Neeman's subcategory $\T_c^-$, and characterize its objects by strong $\E$-coapproximating systems and homotopy inverse limits. Under the compact silting hypothesis, we prove Brown representability theorems identifying $(\T_c^+)^{\op}$ with locally finite $\E$-homological functors and $(\T_c^b)^{\op}$ with finite $\E$-homological functors. We also establish localization results for recollements on the Brown--Comenetz side and derive applications to derived categories of finite-dimensional algebras.

math.RT

Finiteness of homological dimensions in triangulated categories

In a general triangulated category, the finiteness of the finitistic dimension serves as a prerequisite for a categorical obstruction, via the singularity category, to the existence of bounded $t$-structures. In this paper, we investigate the finitistic, big finitistic, and global dimensions, and establish explicit inequalities that relate these dimensions of the middle category in a recollement of triangulated categories to those of the outer categories. This provides a unified framework for extending some known results on the homological dimensions of ordinary rings to weakly approximable triangulated categories.

math.RT

Properties of quasi-projective dimension over abelian categories

Quasi-projective dimension was introduced by Gheibi, Jorgensen and Takahashi to generalize the Auslander-Buchsbaum formula and the depth formula in commutative algebra. In this paper, we establish some basic properties of quasi-projective dimensions of objects in abelian categories. Analogous to global dimension of rings, we also introduce the concept of quasi-global dimension for left Noetherian rings, and then compare quasi-global dimension with global dimension for a class of Nakayama algebras. This provides new examples of finite-dimensional algebras with finite quasi-global dimensions but infinite global dimensions.

math.RA

IRFusionFormer: Enhancing Pavement Crack Segmentation with RGB-T Fusion and Topological-Based Loss

Crack segmentation is crucial in civil engineering, particularly for assessing pavement integrity and ensuring the durability of infrastructure. While deep learning has advanced RGB-based segmentation, performance degrades under adverse conditions like low illumination or motion blur. Thermal imaging offers complementary information by capturing emitted radiation, improving crack detection in challenging environments. Combining RGB and thermal images (RGB-T) for crack segmentation shows promise in complex real-world conditions, such as adverse weather, yet research in this area remains limited. Current RGB-T segmentation methods often fail to fully exploit the complementary relationships between modalities at various levels of interaction. To address this, we propose IRFusionFormer, a novel model for crack segmentation that effectively integrates RGB and thermal data. Our Efficient RGB-T Cross Fusion Module captures multi-scale relationships and long-range dependencies between modalities without significant computational overhead. Additionally, we introduce the Interaction-Hybrid-Branch-Supervision framework, which enhances interaction between modalities by distributing fused features across branches with joint supervision. To maintain the topological structure of cracks, we introduce a novel topology-based loss function that preserves connectivity during training. Our method achieves state-of-the-art performance, with a Dice score of 90.01% and an IoU of 81.83%, significantly improving robustness and accuracy in varying environmental conditions. These advancements address key challenges in pavement crack segmentation, offering a more reliable and efficient solution. For access to the codes, data, and models from this study, visit https://github.com/sheauhuu/IRFusionFormer

cs.CV