Related papers: Model structures for $(\infty,n)$-categories on (p…

We develop a constructive model of homotopy type theory in a Quillen model category that classically presents the usual homotopy theory of spaces. Our model is based on presheaves over the cartesian cube category, a well-behaved…

We show that there is a model structure in the sense of Quillen on an arbitrary Frobenius category $\F$ such that the homotopy category of this model structure is equivalent to the stable category $\underline{\F}$ as triangulated…

For every functor $\mathcal{F} : \mathcal{K} \to \mathbf{C}$, where $\mathcal{K}$ is a small category and $\mathbf{C}$ is a model category which satisfies some mild hypotheses, we define a model category $\mathbf{C}^m$ of…

In the first part of the paper, we prove that the category of diffeological spaces does not admit a model structure transferred via the smooth singular complex functor from simplicial sets, resolving in the negative a conjecture of…

For a small simplicial category A, we prove that the homotopy colimit functor from the category of simplicial diagrams on A to the category of simplicial sets over the homotopy-coherent nerve of A provides a left Quillen equivalence between…

We prove that each of the model structures for ($n$-trivial, saturated) comical sets on the category of marked cubical sets having only faces and degeneracies (without connections) is Quillen equivalent to the corresponding model structure…

A stratified space is a topological space together with a decomposition into strata corresponding to different types of singularities. Examples of such spaces appear everywhere in topology and geometry. The study of stratified spaces…

The filter quotient construction is a particular instance of a filtered colimit of categories. It has primarily been considered in the context of categorical logic, where it has been used effectively to construct non-trivial models, for…

We show how the model structure on the category of simplicially-enriched (colored) props induces a model structure on the category of simplicially-enriched (colored) properads. A similar result holds for dioperads.

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…

The unstraightening construction due to Lurie establishes an equivalence between presheaves and fibrations, using one prominent model of $(\infty,1)$-categories, namely quasi-categories. In this work we generalize this result by proving…

We prove the compatibility between the suspension construction and the complicial nerve of $\omega$-categories. As a motivating application, we produce a Quillen pair between the models of $(\infty,n)$-categories given by Rezk's complete…

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…

It is shown that the Joyal quasi-category model structure for simplicial sets extends to a model structure on simplicial presheaves, for which the weak equivalences are local (or stalkwise) Joyal equivalences.

We construct a cofibrantly generated Quillen model structure on the category of small differential graded categories. ----- Nous construisons une structure de categorie de modeles de Quillen a engendrement cofibrant sur la categorie des…

We construct a cofibrantly generated Quillen model structure on the category of small n-fold categories and prove that it is Quillen equivalent to the standard model structure on the category of simplicial sets. An n-fold functor is a weak…

It has been conjectured since the 1980s that Verity's $n$-complicial sets were a model for $(\infty,n)$-categories. This text is dedicated to providing a positive answer to this conjecture. The proof of this result relies on a thorough…

A simplicial set is said to be non-singular if its non-degenerate simplices are embedded. Let $sSet$ denote the category of simplicial sets. We prove that the full subcategory $nsSet$ whose objects are the non-singular simplicial sets…

Reasoning about weak higher categorical structures constitutes a challenging task, even to the experts. One principal reason is that the language of set theory is not invariant under the weaker notions of equivalence at play, such as…

Let $\bf C$ be a coreflective subcategory of a cofibrantly generated model category $\bf D$. In this paper we show that under suitable conditions $\bf C$ admits a cofibrantly generated model structure which is left Quillen adjunct to the…