论文标题
类别的替代概念：第一部分。
Alternative notion to intercategories: part I. A tricategory of double categories
论文作者
论文摘要
这是两篇论文系列中的第一个。我们的动机是解决Böhm的“双类别的灰色单体产物”中提出的问题：这将是Grandis和Paré类别类别的替代概念，因此Böhm的单体类别$ DBL $ DBL $ dbl $ dbl $ dbl $ dbl $ dbl $ dbl y and double double pseudo and double pseudo是一个示例吗？在解决这个问题之前，我们注意到，尽管嵌入伪双类的生物学，但这种嵌入并不是单一的，通常是单型伪双类别的概念。然后，我们证明了嵌入了Böhm的单人物中的单体生物学。为了将Böhm的Monoid拟合到类别类型的对象中，我们首先将类别$ DBL $升级到2类别，然后最终以tricateGory $ \ dblps $。我们建议将类别作为此曲目中的内部类别的替代定义，使$ dbl $成为此小工具的示例。 （A）tricateGory（of）$ \ dblps $的内部类别的形式定义，以及文献中的另一个重要示例，我们留下了随后的论文。
This is a first of a series of two papers. Our motive is to tackle the question raised in Böhm's "The Gray Monoidal Product of Double Categories" from Applied Categorical Structures: which would be an alternative notion to intercategories of Grandis and Paré, so that monoids in Böhm's monoidal category $Dbl$ of strict double categories and double pseudo functors be an example of it? Before addressing this question we observe that although bicategories embed into pseudo double categories, this embedding is not monoidal, with the usual notion of a monoidal pseudo double category. We then prove that monoidal bicategories embed into the mentioned monoids of Böhm. In order to fit Böhm's monoid into an intercategory-type object, we start by upgrading the category $Dbl$ to a 2-category and end up rather with a tricategory $\DblPs$. We propose an alternative definition of intercategories as internal categories in this tricategory, enabling $Dbl$ to be an example of this gadget. The formal definition of a category internal to the (type of a) tricategory (of) $\DblPs$, as well as another important example of these in the literature, we leave for a subsequent paper.
