论文标题
Batanin对球形代数的方法的扩展
An extension of Batanin's approach to globular algebras
论文作者
论文摘要
在较早的工作中，巴丹宁表明，可以简单地将更高类别的重要定义逮捕，因为在球形套装上。这使他能够概括测谎仪的概念，该概念最初由Street和Burroni对严格的类别引入所有代数Globular较高类别。在这项工作中，我们完善了这一观点，并为此类高级类别介绍了新的结构和属性。特别是，我们定义了细胞延伸的概念及其相关的自由结构，从中，我们从中获得了测谎仪的另一个定义以及球状代数和测谎仪之间的邻接。此外，我们引入了两个标准，允许一个标准使用本文的大多数构造，而无需明确描述基础的球状单子。
In earlier work, Batanin has shown that an important class of definitions of higher categories could be apprehended together simply as monads over globular sets. This allowed him to generalize the notion of polygraph, initially introduced by Street and Burroni for strict categories, to all algebraic globular higher categories. In this work, we refine this perspective and introduce new constructions and properties for this class of higher categories. In particular, we define the notion of cellular extension and its associated free construction, from which we obtain another definition of polygraphs and the adjunction between globular algebras and polygraphs. We moreover introduce two criteria allowing one to use most of the constructions of this article without having to describe explicitly the underlying globular monad.
