广义多范畴的统一框架
A unified framework for generalized multicategories
摘要：
广义多范畴的概念已经在许多文献中被定义，包括对称多范畴、球形运算、Lawvere理论和拓扑空间等不同的例子。在每种情况下，广义多范畴被定义为相对于双范畴上的“单子”的“松弛代数”或“克莱斯利幺半群”。然而，这些词的含义因作者而异，所考虑的具体bicategories也是如此。我们提出了一个统一的框架：通过在双范畴和相关结构（而不是双范畴）上使用单子，人们可以以一种统一所有以前的例子的方式定义广义多范畴，同时简化和澄清大部分理论。
英文摘要：
Notions of generalized multicategory have been defined in numerous contexts throughout the literature, and include such diverse examples as symmetric multicategories, globular operads, Lawvere theories, and topological spaces. In each case, generalized multicategories are defined as the "lax algebras" or "Kleisli monoids" relative to a "monad" on a bicategory. However, the meanings of these words differ from author to author, as do the specific bicategories considered. We propose a unified framework: by working with monads on double categories and related structures (rather than bicategories), one can define generalized multicategories in a way that unifies all previous examples, while at the same time simplifying and clarifying much of the theory.
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