Related papers: Model category structures \`a la Thomason on 2-Cat
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…
The purpose of this article is to present ideas towards obtaining a model category structure on the category of small strict n-categories, generalizing the one obtained by Thomason on ordinary categories. Following ideas of Grothendieck and…
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,…
We study 2-monads and their algebras using a Cat-enriched version of Quillen model categories, emphasizing the parallels between the homotopical and 2-categorical points of view. Every 2-category with finite limits and colimits has a…
In this paper we study a 2-dimensional version of Quillen's homotopy category construction. Given a category $\mathscr{A}$ and a class of morphisms $\Sigma \subset \mathscr{A}$ containing the identities, we construct a 2-category…
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…
This article presents a novel approach to construct a model category structure designed to model the homotopy theory of spaces equipped with an action by the group $C_2$, where morphisms are considered to be isovariant. Our methodology…
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 give the definitions of model bicategory and $q$-homotopy, which are natural generalizations of the notions of model category and homotopy to the context of bicategories. For any model bicategory $\mathcal{C}$, denote by…
We construct a model structure on the category $\mathrm{DblCat}$ of double categories and double functors. Unlike previous model structures for double categories, it recovers the homotopy theory of 2-categories through the horizontal…
Given any model category, or more generally any category with weak equivalences, its simplicial localization is a simplicial category which can rightfully be called the "homotopy theory" of the model category. There is a model category…
In the present article, we describe constructions of model structures on general bicomplete categories. We are motivated by the following question: given a category $\mathcal{C}$ with a subcategory $w\mathcal{C}$ closed under retracts, when…
Given a bicategory C and a family W of arrows of C, we give conditions on the pair (C,W) that allow us to construct the bicategorical localization with respect to W by dealing only with the 2-cells, that is without adding objects or arrows…
A general method for lifting weak factorization systems in a category S to model category structures on simplicial objects in S is described, analogously to the lifting of cotorsion pairs in Abelian categories to model category structures…
To a bicomplex one can associate two natural filtrations, the column and row filtrations, and then two associated spectral sequences. This can be generalized to $N$-multicomplexes. We present a family of model category structures on the…
We show that, for any 2-category $C$ and 2-functor $F\colon C \to Cat$, the double category of elements $\iint_C F$ introduced by Grandis and Par\'e satisfies a version of Thomason's colimit theorem; that is, there is a weak homotopy…
In the last year of his life, Bob Thomason reworked the notion of a model category, used to adapt homotopy theory to algebra, and used homotopy ends to affirmatively solve a problem raised by Grothendieck: find a notion of model structure…
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…
On d\'eveloppe une th\'eorie de l'homotopie des 2-cat\'egories analogue \`a la th\'eorie de l'homotopie des cat\'egories d\'evelopp\'ee par Grothendieck dans "\`A la poursuite des champs". Il s'agit de la th\`ese de doctorat de l'auteur. We…
This paper explores the relationship amongst the various simplicial and pseudo-simplicial objects characteristically associated to any bicategory C. It proves the fact that the geometric realizations of all of these possible candidate…