论文标题
简单的字符串图和n -ssquicategories
Simple string diagrams and n-sesquicategories
论文作者
论文摘要
我们定义一个单子$ t_n^{\ operatoTorname {d^s}} $，其操作由简单的字符串图对其进行编码，我们将$ n $ n $ -sesquicateGories定义为该单片上的代数。该单子编码$ n $维字符串图的组成结构。我们给出了$ t_n^{\ operatorname {d^s}} $的生成器和关系描述，该{\ operatoratorname {d^s}} $，它使我们能够将$ n $ -sesquicateGories描述为$ n $ globular集合，配备了配备了关联和Unitalitive and Unitalitive and unitital和Unital和whiskering操作。一个人也可以将它们视为严格的$ n $类别，而没有互换法律。最后，我们给出了$ n $ -sesquicategories的归纳特征。
We define a monad $T_n^{\operatorname{D^s}}$ whose operations are encoded by simple string diagrams and we define $n$-sesquicategories as algebras over this monad. This monad encodes the compositional structure of $n$-dimensional string diagrams. We give a generators and relations description of $T_n^{\operatorname{D^s}}$ , which allows us to describe $n$-sesquicategories as $n$-globular sets equipped with associative and unital composition and whiskering operations. One can also see them as strict $n$-categories without interchange laws. Finally we give an inductive characterization of $n$-sesquicategories.
