Related papers: Flabby and injective objects in toposes

One challenge that has long held the attention of scientists is that of clearly seeing objects hidden by turbid media, as smoke, fog or biological tissue, which has major implications in fields such as remote sensing or early diagnosis of…

We study the $2$-categories BIon, of (generalized) bounded ionads, and $\text{Acc}_\omega$, of accessible categories with directed colimits, as an abstract framework to approach formal model theory. We relate them to topoi and (lex)…

We introduce the semi-infinite category of sheaves on the affine Grassmannian, and construct a particular object in it, which we call the the semi-infinite intersection cohomology sheaf. We relate it to several other entities naturally…

A generalization of the concept of twisted internal coHom object in the category of conic quantum spaces (c.f. math.QA/0112233) was outlined in math.QA/0202205. The aim of this article is to discuss in more detail this generalization.

We explore functors between operator space categories, some properties of these functors, and establish relations between objects in these categories and their images under these functors, in particular regarding injectivity and injective…

We introduce a pro-\'etale geometric object $D_\infty$ arising naturally from the tower of Artin-Schreier extensions in characteristic 2, equipped with a canonical endofunctor $O$ whose fixed points correspond to automorphic representations…

This paper introduces effectful toposes as an extension of the effective topos and investigates their structure relative to Lawvere-Tierney topologies. First, we formulate effectful toposes by lifting the evidenced frame, which is a…

The Hom closed colocalizing subcategories of the stable module category of a finite group are classified. Along the way, the colocalizing subcategories of the homotopy category of injectives over an exterior algebra, and the derived…

Based on a refinement of the notion of internal sets in Colombeau's theory, so-called strongly internal sets, we introduce the space of generalized smooth functions, a maximal extension of Colombeau generalized functions. Generalized smooth…

The perceived similarity between objects has often been attributed to their physical and conceptual features, such as appearance and animacy, and the theoretical framework of object space is accordingly conceived. Here, we extend this…

B. Tanay et. al. introduced and studied fuzzy soft topological spaces. Here we introduce fuzzy soft point and study the concept of neighborhood of a fuzzy soft point in a fuzzy soft topological space. We also study fuzzy soft closure and…

We combine Homotopy Type Theory with axiomatic cohesion, expressing the latter internally with a version of "adjoint logic" in which the discretization and codiscretization modalities are characterized using a judgmental formalism of "crisp…

A new technique is proposed to classify a topological field in abelian lattice gauge theories. We perform the classification by regarding the topological field as a local composite field of the gauge field tensor instead of the vector…

The purpose of this paper is to introduce the new concept of weighted floating functions associated with log concave or $s$-concave functions. This leads to new notions of weighted functional affine surface areas. Their relation to more…

This paper addresses the challenge of robotic grasping of general objects. Similar to prior research, the task reads a single-view 3D observation (i.e., point clouds) captured by a depth camera as input. Crucially, the success of object…

This paper provides an overview of the applications of sheaf theory in deep learning, data science, and computer science in general. The primary text of this work serves as a friendly introduction to applied and computational sheaf theory…

Grasping, in both biological and engineered mechanisms, can be highly sensitive to the gripper and object morphology, as well as perception, and motion planning. Here we circumvent the need for feedback or precise planning by using an array…

Artificial object perception usually relies on a priori defined models and feature extraction algorithms. We study how the concept of object can be grounded in the sensorimotor experience of a naive agent. Without any knowledge about itself…

Among (isotopy classes of) automorphisms of handlebodies those called irreducible (or generic) are the most interesting, analogues of pseudo-Anosov automorphisms of surfaces. We consider the problem of isotoping an irreducible automorphism…

Motivated by the definition of the smooth manifold structure on a suitable mapping space, we consider the general problem of how to transfer local properties from a smooth space to an associated mapping space. This leads to the notion of…