Dimitri Ara

The Brown-Golasiński model structure on strict ∞-groupoids revisited

We prove that the folk model structure on strict

Higher quasi-categories vs higher Rezk spaces

\infty

The Groupoidal Analogue

-categories transfers to the category of strict

\widetilde{{\Theta}}

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to Joyal’s Category Θ is a Test Category

-groupoids (and more generally to the category of strict

Strict -groupoids are Grothendieck -groupoids

(\infty, n)

Un théorème A de Quillen pour les ∞-catégories strictes I : la preuve simpliciale

-categories), and that the resulting model structure on strict

On the homotopy theory of grothendieck -groupoids

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Vers une structure de catégorie de modèles à la Thomason sur la catégorie des n-catégories strictes

-groupoids coincides with the one defined by Brown and Golasinski via crossed complexes.

On autoequivalences of the

We introduce a notion of n-quasi-categories as fibrant objects of a model category structure on presheaves on Joyals n-cell category \Theta_n. Our definition comes from an idea of Cisinski and Joyal. However, we show that this idea has to be slightly modified to get a reasonable notion. We construct two Quillen equivalences between the model category of n-quasi-categories and the model category of Rezk \Theta_n-spaces showing that n-quasi-categories are a model for (\infty, n)-categories. For n = 1, we recover the two Quillen equivalences defined by Joyal and Tierney between quasi-categories and complete Segal spaces.