Related papers: Flabby and injective objects in toposes
This is an introduction to the notion of local subgroupoid introduced by the author and R. Brown. It can also serve as an introduction to an application of sheaf theory, and so could be useful to beginners in that theory. The main results…
We introduce an axiomatization of Grothendieck sites with additional structure, and we describe sheaves that reconstruct groupoids which are internal to the site structure. This setting applies to various concrete situations, where a Nash…
The homotopy category of a model structure on a weakly idempotent complete additive category is proved to be equivalent to the additive quotient of the category of cofibrant-fibrant objects with respect to the subcategory of…
The goal of this paper is to learn dense 3D shape correspondence for topology-varying objects in an unsupervised manner. Conventional implicit functions estimate the occupancy of a 3D point given a shape latent code. Instead, our novel…
The number of distinguishable inherent structures of a liquid is the key component to understanding the thermodynamics of glass formers. In the case of hard potential systems such as hard discs, spheres and ellipsoids, an inherent structure…
In this paper we introduce the notion of deformation cohomology for singular foliations and related objects (namely integrable differential forms and Nambu structures), and study it in the local case, i.e., in the neighborhood of a point.
We present a generative model of images based on layering, in which image layers are individually generated, then composited from front to back. We are thus able to factor the appearance of an image into the appearance of individual objects…
Given an abelian category, we introduce a categorical concept of (strongly) Gorenstein projective (resp., injective) objects, by defining a new special class of objects. Then we study the transfer of these properties when passing to an…
We show that homotopy pullbacks of sheaves of simplicial sets over a Grothendieck topology distribute over homotopy colimits; this generalizes a result of Puppe about topological spaces. In addition, we show that inverse image functors…
Spatial understanding is a fundamental problem with wide-reaching real-world applications. The representation of spatial knowledge is often modeled with spatial templates, i.e., regions of acceptability of two objects under an explicit…
Simplicial presheaves on cartesian spaces provide a general notion of smooth spaces. There is a corresponding smooth version of the singular complex functor, which maps smooth spaces to simplicial sets. We consider the localisation of the…
We introduce local iterated function systems and present some of their basic properties. A new class of local attractors of local iterated function systems, namely local fractal functions, is constructed. We derive formulas so that these…
Semantic patterns of fine-grained objects are determined by subtle appearance difference of local parts, which thus inspires a number of part-based methods. However, due to uncontrollable object poses in images, distinctive details carried…
Image warping aims to reshape images defined on rectangular grids into arbitrary shapes. Recently, implicit neural functions have shown remarkable performances in representing images in a continuous manner. However, a standalone multi-layer…
To alleviate the cost of obtaining accurate bounding boxes for training today's state-of-the-art object detection models, recent weakly supervised detection work has proposed techniques to learn from image-level labels. However, requiring…
A topos theoretic generalisation of the category of sets allows for modelling spaces which vary according to time intervals. Persistent homology, or more generally, persistence is a central tool in topological data analysis, which examines…
Understanding which inductive biases could be helpful for the unsupervised learning of object-centric representations of natural scenes is challenging. In this paper, we systematically investigate the performance of two models on datasets…
Homotopy Type Theory may be seen as an internal language for the $\infty$-category of weak $\infty$-groupoids which in particular models the univalence axiom. Voevodsky proposes this language for weak $\infty$-groupoids as a new foundation…
Reasoning the human-object interactions (HOI) is essential for deeper scene understanding, while object affordances (or functionalities) are of great importance for human to discover unseen HOIs with novel objects. Inspired by this, we…
The purpose of this paper is to study local cohomology in the noncommutative algebraic geometry framework of Artin and Zhang. The noncommutative spaces are obtained by base change of a Grothendieck category that is locally noetherian or…