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In this paper three results are established: firstly, that the homotopy function complexes of Dwyer and Kan can be defined as certain total right derived functors; secondly, that they functorially compute the homotopy type of the hom-spaces…

Category Theory · Mathematics 2014-09-30 Zhen Lin Low

Given a left Quillen presheaf of localized model structures, we study the homotopy limit model structure on the associated category of sections. We focus specifically on towers and fibered products (pullbacks) of model categories. As…

Algebraic Topology · Mathematics 2017-02-15 Javier J. Gutiérrez , Constanze Roitzheim

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 is a study of Bousfield-Segal spaces, a notion introduced by Julie Bergner drawing on ideas about Eilenberg-Mac Lane objects due to Bousfield. In analogy to Rezk's Segal spaces, they are defined in such a way that Bousfield-Segal…

Algebraic Topology · Mathematics 2021-03-17 Raffael Stenzel

We demonstrate that a Bousfield-Friedlander localization with a set of test morphisms in the sense introduced by Bandklayder, Bergner, Griffiths, Johnson, and Santhanam can also be characterized as a left Bousfield localization at the set…

Algebraic Topology · Mathematics 2025-07-24 Niall Taggart

This paper is the third paper of a series devoted to higher dimensional transition systems. The preceding paper proved the existence of a left determined model structure on the category of cubical transition systems. In this sequel, it is…

Algebraic Topology · Mathematics 2014-01-30 Philippe Gaucher

Homotopical localizations with respect to a set of maps are known to exist in cofibrantly generated model categories (satisfying additional assumptions). In this paper we expand the existing framework, so that it will apply to not…

Algebraic Topology · Mathematics 2007-05-23 Boris Chorny

Building on structure observed in equivariant homotopy theory, we define an equivariant generalization of a symmetric monoidal category: a $G$-symmetric monoidal category. These record not only the symmetric monoidal products but also…

Algebraic Topology · Mathematics 2016-10-12 Michael A. Hill , Michael J. Hopkins

We show that weak equivalences in a (cofibrantly generated) left Bousfield localization of the projective model category of simplicial presheaves can be characterized by a local lifting property if and only if the localization is exact.

Algebraic Topology · Mathematics 2021-04-21 Fritz Hörmann

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…

Category Theory · Mathematics 2007-10-30 Matthew Grime

This paper is part of a series of three articles with the objective of investigating a stratified version of the homotopy hypothesis in terms of semi-model structures that interact well with classical examples of stratified spaces, such as…

Algebraic Topology · Mathematics 2025-01-28 Lukas Waas

In this article we discuss Bousfield localization, beginning with definitions in terms of mapping spaces and working up to a discussion of how they can be constructed when we have access to the small object argument. We also discuss…

Algebraic Topology · Mathematics 2020-02-11 Tyler Lawson

Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal…

Rings and Algebras · Mathematics 2013-08-15 S. Caenepeel , I. Goyvaerts

For a given group $G$ and a collection of subgroups $\mathcal F$ of $G$, we show that there exist a left induced model structure on the category of right $G$-simplicial sets, in which the weak equivalences and cofibrations are the maps that…

Algebraic Topology · Mathematics 2021-02-01 Mehmet Akif Erdal , Aslı Güçlükan İlhan

Given a diagram of rings, one may consider the category of modules over them. We are interested in the homotopy theory of categories of this type: given a suitable diagram of model categories M(s) (as s runs through the diagram), we…

Algebraic Topology · Mathematics 2013-09-27 J. P. C. Greenlees , B. Shipley

We give conditions on a monoidal model category M and on a set of maps C so that the Bousfield localization of M with respect to C preserves the structure of algebras over various operads. This problem was motivated by an example that…

Algebraic Topology · Mathematics 2021-09-01 David White

Covariant Hom-bimodules are introduced and the structure theory of them in the Hom-setting is studied in a detailed way. The category of bicovariant Hom-bimodules is proved to be a (pre)braided monoidal category and its structure theory is…

Quantum Algebra · Mathematics 2019-05-28 Serkan Karaçuha

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…

Algebraic Topology · Mathematics 2009-03-27 Jack Morava

Let $B$ be a bialgebra, and $A$ a left $B$-comodule algebra in a braided monoidal category $\Cc$, and assume that $A$ is also a coalgebra, with a not-necessarily associative or unital left $B$-action. Then we can define a right $A$-action…

Category Theory · Mathematics 2010-11-23 D. Bulacu , S. Caenepeel

The Hom closed colocalizing subcategories of the stable module category of a finite group are classified. Along the way, the colocalizing subcategories of the homotopy category of injectives over an exterior algebra, and the derived…

Representation Theory · Mathematics 2011-02-15 Dave Benson , Srikanth B. Iyengar , Henning Krause