The language of∞-categories provides an insightful new way of expressing many results in
higher-dimensional mathematics but can be challenging for the uninitiated. To explain what …

We axiomatise the theory of $(\infty, n) $-categories. We prove that the space of theories of
$(\infty, n) $-categories is a $ B (\mathbb {Z}/2)^ n $. We prove that Rezk's complete Segal …

This paper develops the foundations of a simplicial theory of weak ω-categories, which
builds upon the insights originally expounded by Ross Street in his 1987 paper on oriented …

We propose four axioms that a quasicategory should satisfy to be considered a reasonable
homotopy theory of (∞, n)-categories. This axiomatization requires that a homotopy theory of …

We prove that the marked triangulation functor from the category of marked cubical sets
equipped with a model structure for (n-trivial, saturated) comical sets to the category of …

The paper focuses on investigating how certain relations between strict $ n $-categories are
preserved in a particular implementation of $(\infty, n) $-categories, given by saturated $ n …

In this paper, we aim to move towards a definition of weak n-category akin to Street's
definition of weak ω-category. This will be accomplished in dimension 1 directly and in …

An important result in quasi-category theory due to Lurie is the that cocartesian fibrations are
exponentiable, in the sense that pullback along a cocartesian fibration admits a right Quillen …

The orientals are the free strict ω-categories on the simplices introduced by Street. The aim
of this paper is to show that they are also the free weak ω-categories on the same …

Résumé Le but de cet article est de démontrer une généralisation pour les∞-catégories
strictes du célèbre théorème A de Quillen. Ce résultat est central à la théorie de l'homotopie …