内部化修饰双范畴：全局生成条件
Internalizing decorated bicategories: The globularily generated condition
摘要：
本文是研究双范畴存在性问题的系列论文的第一部分，给出了双范畴的水平双范畴和对象范畴。我们把这个问题称为修饰双范畴的内在化存在性问题。我们建立了一个正式的框架内，存在的问题，可以正确地制定的内部化。此外，我们引入了一个双重范畴是整体生成的条件。我们证明了一个装饰双范畴的内在化存在性问题允许一个解当且仅当它允许一个整体生成的解，并且我们证明了一个双范畴被整体生成的条件正是一个装饰双范畴的内在化存在性问题的一个解的条件是极小的。因此，对双重范畴是整体生成的条件的研究将是我们研究内在化存在性问题的关键。
英文摘要：
This is the first part of a series of papers studying the problem of existence of double categories for which horizontal bicategory and object category are given. We refer to this problem as the problem of existence of internalizations for decorated bicategories. We establish a formal framework within which the problem of existence of internalizations can be correctly formulated. Further, we introduce the condition of a double category being globularily generated. We prove that the problem of existence of internalizations for a decorated bicategory admits a solution if and only if it admits a globularily generated solution, and we prove that the condition of a double category being globularily generated is precisely the condition of a solution to the problem of existence of internalizations for a decorated bicategory being minimal. The study of the condition of a double category being globularily generated will thus be pivotal in our study of the problem of existence of internalizations.
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