Related papers: Scaled-Free Objects
We systematically derive general properties of continuous and holomorphic functions with values in closed operators, allowing in particular for operators with empty resolvent set. We provide criteria for a given operator-valued function to…
The aim of this article is to study certain categorical-algebraic frameworks for basic homological algebra, introduced in arXiv:2404.15896, with the aim of better understanding the differences between them. We focus on homological…
Alesker's theory of generalized valuations unifies smooth measures and constructible functions on real analytic manifolds, extending classical operations on functions and measures. Alesker showed that these operations agree with the…
Conceptual Scaling is a useful standard tool in Formal Concept Analysis and beyond. Its mathematical theory, as elaborated in the last chapter of the FCA monograph, still has room for improvement. As it stands, even some of the basic…
Given semantic descriptions of object classes, zero-shot learning aims to accurately recognize objects of the unseen classes, from which no examples are available at the training stage, by associating them to the seen classes, from which…
Most existing object detectors suffer from class imbalance problems that hinder balanced performance. In particular, anchor free object detectors have to solve the background imbalance problem due to detection in a per-pixel prediction…
This paper is intended to provide foundations to the theory of Witt-type topological group and ring functors defined on a category of topological algebras, and, in presence of Banach norms, to show how to topologically deal with them. It is…
We introduce and investigate the concept of Stratified Algebra, a new algebraic framework equipped with a layer-based structure on a vector space. We formalize a set of axioms governing intra-layer and inter-layer interactions, study their…
Given an $\infty$-category $\mathcal{C}$ with pullbacks, its $(\infty,2)$-category $\mathbf{Span}(\mathcal{C})$ of spans has the universal property of freely adding right adjoints to morphisms in $\mathcal{C}$ satisfying a Beck--Chevalley…
A classification is provided of functors, in particular polynomial ones, from a category with a zero object in which every object is a finite sum of copies of a generating object, into an abelian category. This classification is extended to…
In various subjects including mathematics, one can hope to use mathematical thinking well when the right kinds of algebraic structure to consider can be discovered or spotted. Therefore, it would help to understand kinds of algebraic…
The FAIR principles are globally accepted guidelines for improved data management practices with the potential to align data spaces on a global scale. In practice, this is only marginally achieved through the different ways in which…
We present a study on the Yoneda-Dress construction of biset functors of linear representations over a field of characteristic zero. We give a characterization of their lattices of ideals and we provide a criterion of vanishing for their…
In the present paper, we propose a new axiomatic approach to nonstandard analysis and its application to the general theory of spatial structures in terms of category theory. Our framework is based on the idea of internal set theory, while…
All physical observations are made relative to a reference frame, which is a system in its own right. If the system of interest admits a group symmetry, the reference frame observing it must transform commensurately under the group to…
A construction analogous to that of Godefroy-Kalton for metric spaces allows to embed isometrically, in a canonical way, every quasi-metric space $(X,d)$ to an asymmetric normed space $\mathcal{F}_a(X,d)$ (its quasi-metric free space, also…
Structures where we have both a contravariant (pullback) and a covariant (pushforward) functoriality that satisfy base change can be encoded by functors out of ($\infty$-)categories of spans (or correspondences). In this paper we study the…
In this work we investigate the transfer of fundamental order and completeness properties between truncated Riesz spaces and their unitizations. Specifically, we provide characterizations and equivalences for several notions of…
In the paper "Triangulations, orientals, and skew monoidal categories", the free monoidal category Fsk on a single generating object was described. We sharpen this by giving a completely explicit description of Fsk, and so of the free skew…
In this paper, we develop the proof theory of skew prounital closed categories. These are variants of the skew closed categories of Street where the unit is not represented. Skew closed categories in turn are a weakening of the closed…