Related papers: An introduction to Bousfield localization
We give an account of Bousfield localisation and colocalisation for one-dimensional model categories---ones enriched over the model category of $0$-types. A distinguishing feature of our treatment is that it builds localisations and…
This is the introductory chapter to the volume. We review the main idea of the localization technique and its brief history both in geometry and in QFT. We discuss localization in diverse dimensions and give an overview of the major…
We prove the equivalence of several hypotheses that have appeared recently in the literature for studying left Bousfield localization and algebras over a monad. We find conditions so that there is a model structure for local algebras, so…
This paper is a companion for the paper "Monoidal Bousfield Localizations and Algebras over Operads," part of the author's PhD thesis. This paper was written in 2015 for the first edition of "Enchiridion: Mathematics User's Guides." More…
We provide a complete description of the model category structures on the nonmodular lattice $N_5$. Furthermore we explain how these model category structures are related to each other via Bousfield localization. This work heavily relies on…
Consider a Quillen adjunction of two variables between combinatorial model categories from $\mathcal{C}\times\mathcal{D}$ to $\mathcal{E}$, and a set $\mathcal{S}$ of morphisms in $\mathcal{C}$. We prove that there is a localised model…
It is well known that under some general conditions right Bousfield localization exists. We provide general conditions under which right Bousfield localization yields a monoidal model category. Then we address the questions of when this…
We compute the Bousfield localizations and Bousfield colocalizations of discrete model categories, including the homotopy categories and the algebraic $K$-groups of these localizations and colocalizations. We prove necessary and sufficient…
We develop the theory of locally small spaces in a new simple language and apply this simplification to re-build the theory of locally definable spaces over structures with topologies.
In this article we introduce the notion of a square structure on a model category, that generalises cubical model categories. We then show that under some homotopical conditions on this square structure the induced cubical category is a…
The goal of object detection is to find objects in an image. An object detector accepts an image and produces a list of locations as $(x,y)$ pairs. Here we introduce a new concept: {\bf location-based boosting}. Location-based boosting…
I verify the existence of left Bousfield localizations and of enriched left Bousfield localizations, and I prove a collection of useful technical results characterizing certain fibrations of (enriched) left Bousfield localizations. I also…
Our main motivation for the work presented in this paper is to construct a localization functor, in a certain sense dual to the f-localization of Bousfield and Farjoun, and to study some of its properties. We succeed in a case which is…
We compare several recent approaches to studying right Bousfield localization and algebras over monads. We prove these approaches are equivalent, and we apply this equivalence to obtain several new results regarding right Bousfield…
Model categories have long been a useful tool in homotopy theory, allowing many generalizations of results in topological spaces to other categories. Giving a localization of a model category provides an additional model category structure…
This is the foreword to the special volume on localization techniques in quantum field theory. We summarize the individual chapters and their relation.
We prove a new localization theorem for stable model categories if the localizing subcategory is generated by a precovering class in the model category. We use this to show how one may explicitly realize certain Bousfield localization…
In this article, we develop and investigate a new classifier based on features extracted using spatial depth. Our construction is based on fitting a generalized additive model to the posterior probabilities of the different competing…
Using the dual of Bousfield-Friedlander localization we colocalize resolution model structures on cosimplicial objects over a left proper model category to get truncated resolution model structures. These are useful to study realization and…
The localization phenomena due to the random potential scattering is widely discussed in the electron and photon systems, where the theoretical approach is the nonlinear $\sigma$ model with the replica method or with the supersymmetry. In…