Algebraic Definition of weak ($\infty$; n)-Categories

Abstract

In this paper we define a sequence of monads ${\mathbb{T}}^{(}\infty ;n)$ $(n\in \mathbb{N})$ on $\infty$-$\mathbb{G}\text{r}$, the category of the $\infty$-graphs. We conjecture that algebras for ${\mathbb{T}}^{(}0;n)$ which are defined in a purely algebraic setting, are models of weak $\infty$-groupoids. And for all $n>1$ we conjecture that algebras for ${\mathbb{T}}^{(}\infty ;n)$ which are defined in a purely algebraic setting, are models of weak $(\infty ;n)$-categories.

38 pages

References in corpus (1)

• Higher Topos Theory