弱（$\infty$ ; n）-范畴的代数定义
Algebraic Definition of weak ($\infty$; n)-Categories
摘要：
本文在$\infty$ -图的范畴$\infty$ - $\mathbb{G}\text{r}$上定义了单子序列$\mathbb{T}^(\infty;n)$ $(n\in\mathbb{N})$.我们猜想定义在纯代数环境中的$\mathbb{T}^(0;n)$的代数是弱$\infty$ -广群胚的模型。对于所有的$n>1$，我们猜想定义在纯代数环境中的$\mathbb{T}^(\infty;n)$的代数是弱$(\infty; n)$ -范畴的模型.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
