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citeseer: CiteSeer citations (2014)
Citations among papers indexed by the CiteSeer digital library. If a paper i cites a paper j also in this data set, then a directed edge connects i to j. (Papers not in the data set are excluded.) Self-loops may be present.
This network has 384413 nodes and 1751463 edges.
Tags: Informational, Citation, Unweighted

Quantaloid-enriched categories: Factorization, weak classifiers, and symmetry
Javier Guti\'errez Garc\'ia, Ulrich H\"ohle
https://arxiv.org/abs/2510.10162 https://

Quantaloid-enriched categories: Factorization, weak classifiers, and symmetry
This paper provides a comprehensive overview of some of the foundational properties of categories enriched over quantaloids, along with several new results. We demonstrate that the category whose objects are quantaloid-enriched categories and whose morphisms are left adjoint distributors admits an (epi, extremal mono)--factorization system. Furthermore, we prove that the category of cocomplete quantaloid-enriched categories satisfies the weak subobject classifier axiom, under stability conditio…

Oriented Category Theory
David Gepner, Hadrian Heine
https://arxiv.org/abs/2510.10504 https://arxiv.org/pdf/2510.10504

Oriented Category Theory
We develop foundations for oriented category theory, an extension of $(\infty,\infty)$-category theory obtained by systematic usage of the Gray tensor product, in order to study lax phenomena in higher category theory. As categorical dimension increases, classical category-theoretic concepts generally prove too rigid or fully break down and must be replaced by oriented versions, which allow more flexible notions of naturality and coherence. Oriented category theory provides a framework to addre…

Homological epimorphisms in functor categories and singularity categories
Juan Andr\'es Orozco Guti\'errez, Valente Santiago Vargas
https://arxiv.org/abs/2510.09855 http…

Homological epimorphisms in functor categories and singularity categories
Given a homological epimorphism $π:\mathcal{C}\longrightarrow \mathcal{C}/\mathcal{I}$ between $K$-categories, we show that if the ideal $\mathcal{I}$ satisfies certain conditions, then there exists an equivalence between the singularity categories $\mathbf{D}_{sg}(\mathrm{Mod}(\mathcal{C}))$ and $ \mathbf{D}_{sg}(\mathrm{Mod}(\mathcal{C}/\mathcal{I}))$. This result generalizes the one obtained by Xiao-Wu Chen in [6]. We apply our result to the one point extension category and show that there …

Beyond 'Templates': Category-Agnostic Object Pose, Size, and Shape Estimation from a Single View
Jinyu Zhang, Haitao Lin, Jiashu Hou, Xiangyang Xue, Yanwei Fu
https://arxiv.org/abs/2510.11687

Beyond 'Templates': Category-Agnostic Object Pose, Size, and Shape Estimation from a Single View
Estimating an object's 6D pose, size, and shape from visual input is a fundamental problem in computer vision, with critical applications in robotic grasping and manipulation. Existing methods either rely on object-specific priors such as CAD models or templates, or suffer from limited generalization across categories due to pose-shape entanglement and multi-stage pipelines. In this work, we propose a unified, category-agnostic framework that simultaneously predicts 6D pose, size, and dense sha…

Natural transformations between braiding functors in the Fukaya category
Yujin Tong
https://arxiv.org/abs/2511.10462 https://arxiv.org/pdf/2511.10462 https://arxiv.org/html/2511.10462
arXiv:2511.10462v1 Announce Type: new
Abstract: We study the space of $A_\infty$-natural transformations between braiding functors acting on the Fukaya category associated to the Coulomb branch $\mathcal{M}(\bullet,1)$ of the $\mathfrak{sl}_2$ quiver gauge theory. We compute all cohomologically distinct $A_\infty$-natural transformations $\mathrm{Nat}(\mathrm{id}, \mathrm{id})$ and $\mathrm{Nat}(\mathrm{id}, \beta_i^-)$, where $\beta_i^-$ denotes the negative braiding functor. Our computation is carried out in a diagrammatic framework compatible with the established embedding of the KLRW category into this Fukaya category. We then compute the Hochschild cohomology of the Fukaya category using an explicit projective resolution of the diagonal bimodule obtained via the Chouhy-Solotar reduction system, and use this to classify all cohomologically distinct natural transformations. These results determine the higher $A_\infty$-data encoded in the braiding functors and their natural transformations, and provide the first step toward a categorical formulation of braid cobordism actions on Fukaya categories.
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Universal properties of Delannoy categories
Kevin Coulembier, Nate Harman, Andrew Snowden
https://arxiv.org/abs/2510.10317 https://arxiv.org/pdf/2510.10317…

Universal properties of Delannoy categories
Recently, the second and third authors introduced a new symmetric tensor category $\underline{\mathrm{Perm}}(G, μ)$ associated to an oligomorphic group $G$ with a measure $μ$. When $G$ is the group of order preserving self-bijections of the real line there are four such measures, and the resulting tensor categories are called the Delannoy categories. The first Delannoy category is semi-simple, and was studied in detail by Harman, Snowden, and Snyder. We give universal properties for all four …

citeseer: CiteSeer citations (2014)
Citations among papers indexed by the CiteSeer digital library. If a paper i cites a paper j also in this data set, then a directed edge connects i to j. (Papers not in the data set are excluded.) Self-loops may be present.
This network has 384413 nodes and 1751463 edges.
Tags: Informational, Citation, Unweighted

Some Properties of Homology and Exactness of Nomura's Homology Sequences in a Grandis Homological Category
Yaroslav Kopylov, Vadim Leshkov
https://arxiv.org/abs/2510.11672 h…

Some Properties of Homology and Exactness of Nomura's Homology Sequences in a Grandis Homological Category
We consider Lambek's invariants $\text{Ker}$ and $\text{Im}$ for commutative squares in Grandis homological categories. We prove that Nomura's null sequences exist in such categories and find sufficienct conditions for their exactness. We also prove the coincidence of left and right homology in Grandis homological categories.