相关论文: The orthogonal subcategory problem in homotopy the…

Constructions of spectra from symmetric monoidal categories are typically functorial with respect to strict structure-preserving maps, but often the maps of interest are merely lax monoidal. We describe conditions under which one can…

This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the…

In this paper, we consider the model structure on the category of cellular sets originally conjectured by Cisinski and Joyal to give a model for the homotopy theory of weak (\omega)-categories. We demonstrate first that any…

We prove the Derived Mapping Space Lemma, which generalizes the central theorem of Cisinski's work on calculus of fractions for $\infty$-categories, and allows us to provide a unified framework for analyzing mapping spaces in localizations…

In this paper we develop homotopy theoretical methods for studying diagrams. In particular we explain how to construct homotopy colimits and limits in an arbitrary model category. The key concept we introduce is that of a model…

In "On o-minimal homotopy groups", o-minimal homotopy was developed for the definable category, proving o-minimal versions of the Hurewicz theorems and the Whitehead theorem. Here, we extend these results to the category of locally…

In homotopy theory, exact sequences and spectral sequences consist of groups and pointed sets, linked by actions. We prove that the theory of such exact and spectral sequences can be established in a categorical setting which is based on…

In this article we consider the homotopy theory of stratified spaces through a simplicial point of view. We first consider a model category of filtered simplicial sets over some fixed poset $P$, and show that it is a simplicial…

We show that the classifying space functor $B: Mon \to Top*$ from the category of topological monoids to the category of based spaces is left adjoint to the Moore loop space functor $\Omega': Top*\to Mon$ after we have localized $Mon$ with…

This text develops a homotopy theory of 2-categories analogous to Grothendieck's homotopy theory of categories developed in "Pursuing Stacks". We define the notion of "basic localizer of 2-Cat", 2-categorical generalization of…

Our main result states that for each finite complex L the category ${\bf TOP}$ of topological spaces possesses a model category structure (in the sense of Quillen) whose weak equivalences are precisely maps which induce isomorphisms of all…

Given a locally presentable category together with a suitable functorial cylinder object, we construct model structures which are sensitive to the `direction' of the cylinder. We show that the Covariant and Contravariant model structures on…

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…

Given a functor $\varphi : \mathcal{C} \to \mathcal{D}$ between two small categories, there is a homotopy equivalence $\kappa: hocolim _{\mathcal{D}} N(\varphi /-) \to N\mathcal{C}$ where $N(\varphi/-)$ is the functor which sends every…

This is a sequel to a previous paper, developing an intrinsic, combinatorial homotopy theory for simplicial complexes; the latter form the cartesian closed subcategory of 'simple presheaves' in !Smp, the topos of symmetric simplicial sets,…

We decompose the K-theory space of a Waldhausen category in terms of its Dwyer-Kan simplicial localization. This leads to a criterion for functors to induce equivalences of K-theory spectra that generalizes and explains many of the criteria…

We construct a "diagonal" cofibrantly generated model structre on the category of simplicial objects in the category of topological categories sCat_{Top}, which is the category of diagrams [\Delta^{op}, Cat_{Top}]. Moreover, we prove that…

We give a new criterion guaranteeing existence of model structures left-induced along a functor admitting both adjoints. This works under the hypothesis that the functor induces idempotent adjunctions at the homotopy category level. As an…

The aim of this paper is to show that the most elementary homotopy theory of $\mathbf{G}$-spaces is equivalent to a homotopy theory of simplicial sets over $\mathbf{BG}$, where $\mathbf{G}$ is a fixed group. Both homotopy theories are…

If all objects of a simplicial combinatorial model category \cat A are cofibrant, then there exists the homotopy model structure on the category of small functors $\sS^{\cat A}$, where the fibrant objects are homotopy functors, i.e.,…