论文标题
$ n $ -sesquicateGories的computads and String图
Computads and string diagrams for $n$-sesquicategories
论文作者
论文摘要
$ n $ -sesquicateGory是$ n $ blobular套装，具有严格的关联和Unital构图和搅拌操作，但是，不需要满足$ n $类别的Godement交换法律。在ARXIV：2202.09293中，我们展示了如何将其定义为单调的代数$ t_n^{d^s} $，其操作是简单的字符串图。在本文中，我们对Monad $ t_n^{d^s} $的Computads进行了明确的描述，我们证明了该单月的Computads类别是Presheaf类别。我们用它来描述用于表示$ n $ -sesquicateGorie中任意复合材料的字符串图符号。这是迈向半分布图$ n $类别的字符串图理论的一步。
An $n$-sesquicategory is an $n$-globular set with strictly associative and unital composition and whiskering operations, which are however not required to satisfy the Godement interchange laws which hold in $n$-categories. In arXiv:2202.09293 we showed how these can be defined as algebras over a monad $T_n^{D^s}$ whose operations are simple string diagrams. In this paper, we give an explicit description of computads for the monad $T_n^{D^s}$ and we prove that the category of computads for this monad is a presheaf category. We use this to describe a string diagram notation for representing arbitrary composites in $n$-sesquicategories. This is a step towards a theory of string diagrams for semistrict $n$-categories.
