相关论文: Handle Slides and Localizations of Categories

We extend the framework of combinatorial model categories, so that the category of small presheaves over large indexing categories and ind-categories would be embraced by the new machinery called class-combinatorial model categories. The…

We consider the problem of classifying trajectories on a discrete or discretised 2-dimensional manifold modelled by a simplicial complex. Previous works have proposed to project the trajectories into the harmonic eigenspace of the Hodge…

Object detection or localization is an incremental step in progression from coarse to fine digital image inference. It not only provides the classes of the image objects, but also provides the location of the image objects which have been…

We classify the prelocalizing subcategories of the category of quasi-coherent sheaves on a locally noetherian scheme. In order to give the classification, we introduce the notion of a local filter of subobjects of the structure sheaf. The…

Pronk's theorem on bicategories of fractions is applied, in almost all cases in the literature, to 2-categories of geometrically presentable stacks on a 1-site. We give an proof that subsumes all previous such results and which is purely…

The purpose of this paper is to study categorifications of tensor products of finite dimensional modules for the quantum group for sl(2). The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie…

A handlebody-knot is a handlebody embedded in the 3-sphere. We establish a uniform method to construct invariants for handlebody-links. We introduce the category $\mathcal{T}$ of handlebody-tangles and present it by generators and…

A new approach is suggested to the problem of quantising causal sets, or topologies, or other such models for space-time (or space). The starting point is the observation that entities of this type can be regarded as objects in a category…

The motion of deformable 4D objects lies in a low-dimensional manifold. To better capture the low dimensionality and enable better controllability, traditional methods have devised several heuristic-based methods, i.e., rigging, for…

Category-level articulated object pose estimation aims to estimate a hierarchy of articulation-aware object poses of an unseen articulated object from a known category. To reduce the heavy annotations needed for supervised learning methods,…

A subunit in a monoidal category is a subobject of the monoidal unit for which a canonical morphism is invertible. They correspond to open subsets of a base topological space in categories such as those of sheaves or Hilbert modules. We…

We construct quantum $\mathcal{U}_q(\mathfrak{sl}_{\,2})$ type invariants for handlebody-knots in the 3-sphere $S^3$. A handlebody-knot is an embedding of a handlebody in a 3-manifold. These invariants are linear sums of Yokota's invariants…

In two recent papers by the author, a new approach was suggested for quantising space-time, or space. This involved developing a procedure for quantising a system whose configuration space--or history-theory analogue--is the set of objects,…

We describe all the localization observables of a quantum particle in a one-dimensional box in terms of sequences of unit vectors in a Hilbert space. An alternative representation in terms of positive semidefinite complex matrices is…

Restriction categories provide a categorical framework for partiality. In this paper, we introduce three new categorical theories for partiality: local categories, partial categories, and inclusion categories. The objects of a local…

The Hom closed colocalising subcategories of the stable module category of a finite group scheme are classified. This complements the classification of the tensor closed localising subcategories in our previous work. Both classifications…

Visual affordance segmentation identifies the surfaces of an object an agent can interact with. Common challenges for the identification of affordances are the variety of the geometry and physical properties of these surfaces as well as…

In this paper, we introduce a deformation analysis of index theory over non compact manifolds, by use of new functional spaces which are the reduced version of Sobolev spaces. It allows to construct Fredholm theory for elliptic differential…

One can represent Schwartz distributions with values in a vector bundle $E$ by smooth sections of $E$ with distributional coefficients. Moreover, any linear continuous operator which maps $E$-valued distributions to smooth sections of…

We introduce the notion of a quandle with a good involution and its homology groups. Carter et al. defined quandle cocycle invariants for oriented links and oriented surface-links. By use of good involutions, quandle cocyle invariants can…