Related papers: Constructing model categories with prescribed fibr…

In a previous work, we have introduced a weakening of Quillen model categories called weak model categories. They still allow all the usual constructions of model category theory, but are easier to construct and are in some sense better…

This expository article sets forth a self-contained and purely algebraic proof of a deep result of Quillen stating that the category of simplicial commutative algebras over a commutative ring is a model category. This is accomplished by…

In this monograph, we extend S. Schwede's exact sequence interpretation of the Gerstenhaber bracket in Hochschild cohomology to certain exact and monoidal categories. Therefore we establish an explicit description of an isomorphism by A.…

This paper is a contribution to the construction of non-semisimple modular categories. We establish when M\"uger centralizers inside non-semisimple modular categories are also modular. As a consequence, we obtain conditions under which…

We propose a new model for the theory of $(\infty,n)$-categories (including the case $n=\infty$) in the category of marked cubical sets with connections, similar in flavor to complicial sets of Verity. The model structure characterizing our…

The long hunt for a symmetric monoidal category of spectra finally ended in success with the simultaneous discovery of the third author's discovery of symmetric spectra and the Elmendorf-Kriz-Mandell-May category of S-modules. In this paper…

We prove the existence of Morita model structures on the categories of small simplicial categories, simplicial sets, simplicial operads and dendroidal sets, modelling the Morita homotopy theory of $(\infty,1)$-categories and…

We prove existence results for small presentations of model categories generalizing a theorem of D. Dugger from combinatorial model categories to more general model categories. Some of these results are shown under the assumption of…

Let k be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of k-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a…

We show that Quillen's small object argument works for exact categories under very mild conditions. This has immediate applications to cotorsion pairs and their relation to the existence of certain triangulated adjoint functors and model…

We show that the fibrant objects in the minimal model structure on the category of simplicial sets are characterized by a lifting condition with respect to maps which resemble the horn inclusions that define Kan complexes.

We construct a discrete model of the homotopy theory of $S^1$-spaces. We define a category $\sP$ with objects composed of a simplicial set and a cyclic set along with suitable compatibility data. $\sP$ inherits a model structure from the…

We investigate fibrancy conditions in the Thomason model structure on the category of small categories. In particular, we show that the category of weak equivalences of a partial model category is fibrant. Furthermore, we describe…

We construct on the category of diffeological spaces a Quillen model structure having smooth weak homotopy equivalences as the class of weak equivalences.

In this paper we prove that for any simplicial set $B$, there is a Quillen equivalence between the covariant model structure on $\mathbf{S}/B$ and a certain localization of the projective model structure on the category of simplicial…

We formulate the concept of minimal fibration in the context of fibrations in the model category $\mathbf{S}^\mathcal{C}$ of $\mathcal{C}$-diagrams of simplicial sets, for a small index category $\mathcal{C}$. When $\mathcal{C}$ is an…

We define a new model structure on the category of small categories, which is intimately related to the notion of coverings and fundamental groups of small categories. Fibrant objects in the model structure coincide with groupoids, and the…

We build a model structure from the simple point of departure of a structured interval in a monoidal category - more generally, a structured cylinder and a structured co-cylinder in a category.

We produce a cofibrantly generated simplicial symmetric monoidal model structure for the category of (small unital) C*-categories, whose weak equivalences are the unitary equivalences. The closed monoidal structure consists of the maximal…

In [Homotopical Algebra, Springer LNM 43] Quillen introduces the notion of a model category: a category $\mathcal{C}$ provided with three distinguished classes of maps $\{\mathcal{W},\, \mathcal{F},\, co\mathcal{F}\}$ (weak equivalences,…