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Related papers: An introduction to Bousfield localization

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We examine various triangulated quotients of the module category of a finite group. We demonstrate that these are not compactly generated by the simple modules and present a modification of Rickard's Idempotent Module construction that…

Representation Theory · Mathematics 2007-05-23 Matthew Grime

We develop the theory of nilpotent $G$-spaces and their localisations, for $G$ a compact Lie group, via reduction to the non-equivariant case using Bousfield localisation. One point of interest in the equivariant setting is that we can…

Algebraic Topology · Mathematics 2024-10-29 Andrew Ronan

We develop the notion of left and right Bousfield localizations in proper, cellular symmetric monoidal model categories with cofibrant unit, using homotopy function complexes defined by internal Hom objects instead of Hom sets.

Category Theory · Mathematics 2021-08-23 Renaud Gauthier

This article is a brief introduction to the rapidly evolving field of many-body localization. Rather than giving an in-depth review of the subject, our aspiration here is simply to introduce the problem and its general context, outlining a…

Disordered Systems and Neural Networks · Physics 2017-08-02 Dmitry A. Abanin , Zlatko Papić

We show that several apparently unrelated formulas involving left or right Bousfield localizations in homotopy theory are induced by comparison maps associated with pairs of adjoint functors. Such comparison maps are used in the article to…

Algebraic Topology · Mathematics 2022-05-06 Carles Casacuberta , Oriol Raventós , Andrew Tonks

We construct combinatorial model category structures on the categories of (marked) categories and (marked) pre-additive categories, and we characterize (marked) additive categories as fibrant objects in a Bousfield localization of…

Algebraic Topology · Mathematics 2021-05-28 Ulrich Bunke , Alexander Engel , Daniel Kasprowski , Christoph Winges

The location determination in obstructed area can be very challenging especially if Global Positioning System are blocked. Users will find it difficult to navigate directly on-site in such condition, especially indoor car park lot or…

Human-Computer Interaction · Computer Science 2011-03-28 Wan Mohd. Yaakob Wan Bejuri , Mohd. Murtadha Mohamad , Maimunah Sapri

We adopt semimodel categories to extend fundamental results related to Bousfield localizations of model categories. More specifically, we generalize Bousfield-Friedlander Theorem and Hirschhorn Localization Theorem of cellular model…

Algebraic Topology · Mathematics 2022-09-21 Victor Carmona

We give a moderately motivated exposition of exponentiable locales and the construction of exponentials in $\textsf{Loc}$, without assuming prior knowledge of exponential topological spaces or continuous posets.

General Topology · Mathematics 2025-07-22 Xu Huang

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…

Logic · Mathematics 2019-08-20 Russell Miller

In this paper we define and compare several new Quillen model structures which present the homotopy theory of algebraic quantum field theories. In this way, we expand foundational work of Benini et al. by providing a richer framework to…

Mathematical Physics · Physics 2023-02-16 Victor Carmona

This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…

General Topology · Mathematics 2023-09-06 Melih İs

While topology given by a linear order has been extensively studied, this cannot be said about the case when the order is given only locally. The aim of this paper is to fill this gap. We consider relation between local orderability and…

General Topology · Mathematics 2020-09-17 Piotr Pikul

We introduce a construction adding low-dimensional cells to a space that satisfies certain low-dimensional conditions; it preserves high-dimensional homology with appropriate coefficients. This includes as special cases Quillen's plus…

K-Theory and Homology · Mathematics 2013-01-30 Shengkui Ye

Iterated localization is considered where each node of a network needs to get localized (find its location on 2-D plane), when initially only a subset of nodes have their location information. The iterated localization process proceeds as…

Information Theory · Computer Science 2012-05-23 Rahul Vaze , Piyush Gupta

The purpose of this paper is to establish the foundations of multi-microlocalization, in particular, to give the fiber formula for the multi-microlocalization functor and estimate of microsupport of a multi-microlocalized object. We also…

Algebraic Geometry · Mathematics 2014-01-07 Naofumi Honda , Luca Prelli , Susumu Yamazaki

The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…

General Topology · Mathematics 2018-04-13 Wanjun Hu

The aim of this paper is to introduce the concepts of homotopical smallness and closeness. These are the properties of homotopical classes of maps that are related to recent developments in homotopy theory and to the construction of…

Geometric Topology · Mathematics 2011-01-05 Ziga Virk

Framings provide a way to construct Quillen functors from simplicial sets to any given model category. A more structured set-up studies stable frames giving Quillen functors from spectra to stable model categories. We will investigate how…

Algebraic Topology · Mathematics 2011-07-21 David Barnes , Constanze Roitzheim

This paper is about enabling robots to improve their perceptual performance through repeated use in their operating environment, creating local expert detectors fitted to the places through which a robot moves. We leverage the concept of…

Robotics · Computer Science 2017-08-14 Jeffrey Hawke , Alex Bewley , Ingmar Posner