Tootfinder

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…

From Abelianization to Tangent Categories
Sacha Ikonicoff, Jean-Simon Pacaud Lemay, Tim Van der Linden
https://arxiv.org/abs/2510.12324 https://arxiv.org/p…

From Abelianization to Tangent Categories
A tangent category is a category with an endofunctor, called the tangent bundle functor, which is equipped with various natural transformations that capture essential properties of the classical tangent bundle of smooth manifolds. In this paper, we show that, surprisingly, the category of groups is a tangent category whose tangent bundle functor is induced by abelianization and whose differential bundles correspond to abelian groups. We generalize this construction by introducing the concept of…

Derived mapping spaces of $\infty$-categories
Kensuke Arakawa, Daniel Carranza, Chris Kapulkin
https://arxiv.org/abs/2509.10288 https://arxiv.org/pdf/2509.…

Derived mapping spaces of $\infty$-categories
We prove the Derived Mapping Space Lemma, which generalizes the central theorem of Cisinski's work on calculus of fractions for $\infty$-categories, and allows us to provide a unified framework for analyzing mapping spaces in localizations of ($\infty$-)categories. As an application, we give a sufficient condition for when a cubical or simplicial category is the localization of its underlying category at homotopy equivalences.

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 …

A Categorical Approach to Finiteness Conditions
David Forsman
https://arxiv.org/abs/2509.10204 https://arxiv.org/pdf/2509.10204

A Categorical Approach to Finiteness Conditions
We introduce a general categorical framework for finiteness conditions that unifies classical notions such as Noetherianness, Artinianness, and various forms of topological compactness. This is achieved through the concept of \textbf{$τ$-compactness}, defined relative to a \textbf{coverage} $τ$. A coverage on a category $C$ is a specified class of covering diagrams, which are functors $F\colon I \to C/c$ of a specified variance, where the indexing category $I$ is equipped with a set of 'desig…

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.