Related papers: Localization theory for triangulated categories
Moralisation and Triangulation are transformations allowing to switch between different ways of factoring a probability distribution into a graphical model. Moralisation allows to view a Bayesian network (a directed model) as a Markov…
Dynamical localization is a localization phenomenon taking place, for example, in the quantum periodically-driven kicked rotor. It is due to subtle quantum destructive interferences and is thus of intrinsic quantum origin. It has been shown…
We consider $(\infty,d)$-categories in the limit $d\to \infty$ via the core or localization functors that forget or invert higher non-invertible arrows, respectively. We compare the two resulting $(\infty,1)$-categories of…
We discuss the notion of linearization through examples, which include the Price map, PageRank, representation theory, the Euler characteristic and quantum invariants. We also review categorification, which adds an additional layer of…
This paper lays the groundwork for the theory of categorical diagonalization. Given a diagonalizable operator, tools in linear algebra (such as Lagrange interpolation) allow one to construct a collection of idempotents which project to each…
We use double categories to obtain a single theorem characterizing certain exponentiable morphisms of small categories, topological spaces, locales, and posets.
Recently, virtual reality, augmented reality, robotics, autonomous driving et al attract much attention of both academic and industrial community, in which image based camera localization is a key task. However, there has not been a…
This very speculative sketch suggests that a theory of fundamental groupoids for tensor triangulated categories could be used to describe the ring of integers as the singular fiber in a family of ring-spectra parametrized by a structure…
This paper studies 3-D distributed network localization using mixed types of local relative measurements. Each node holds a local coordinate frame without a common orientation and can only measure one type of information (relative position,…
This paper presents a unified approach for localizing some relevant graph topological indices via majorization techniques. Through this method, old and new bounds are derived and numerical examples are provided, showing how former results…
A recollement of triangulated categories describes one such category as being "glued together" from two others. This paper gives a precise criterion for the existence of a recollement of the derived category of a Differential Graded Algebra…
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 develop an extension of institution theory that accommodates implicitly the partiality of the signature morphisms and its syntactic and semantic effects. This is driven primarily by applications to conceptual blending, but other…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
We construct an iterative method for factorising small strict n-categories into a unique (up to isomorphism) collection of small 1- categories. Following this we develop the theory to include a large class of $\infty$-categories. We use…
We present a generalization of multiview varieties as closures of images obtained by projecting subspaces of a given dimension onto several views, from the photographic and geometric points of view. Motivated by applications in Computer…
Given a pair of adjoint functors between two arbitrary categories it induces mutually inverse equivalences between the full subcategories of the initial ones, consisting of objects for which the arrows of adjunction are isomorphisms. We…
For a finite dimensional algebra $A$, we establish correspondences between torsion classes and wide subcategories in $mod(A)$. In case $A$ is representation finite, we obtain an explicit bijection between these two classes of subcategories.…
In [1] we introduced the concept of structured space, which is a topological space that locally resembles some algebraic structures. In [2] we proceeded the study of these spaces, developing two cohomology theories. The aim of this paper is…
Category theory has foundational importance because it provides conceptual lenses to characterize what is important in mathematics. Originally the main lenses were universal mapping properties and natural transformations. In recent decades,…