论文标题
东方作为自由代数
Orientals as free algebras
论文作者
论文摘要
本文的目的是基于Burroni的想法，即Orientals在严格的$ω$ - 类别上为某些代数结构提供了自由代数。更确切地说，在Burroni之后，我们定义了$ω$ - 类别的扩展概念，并且我们表明，从严格的$ω$ - 类别中的健忘函数赋予了扩展到严格的$ω$类别的扩展。通过从空的$ω$ - 类别开始迭代此单片，我们在严格的$ω$类别中获得了一个cosimimplicial对象。我们的主要贡献是表明，这个cosimplicial对象是东方的cosimimplicial对象。为此，我们使用Steiner的增强定向链复合物理论证明，这是比较具有相同发电机和相同线性化源和目标的测谎仪的一般结果。
The aim of this paper is to give an alternative construction of Street's cosimplicial object of orientals, based on an idea of Burroni that orientals are free algebras for some algebraic structure on strict $ω$-categories. More precisely, following Burroni, we define the notion of an expansion on an $ω$-category and we show that the forgetful functor from strict $ω$-categories endowed with an expansion to strict $ω$-categories is monadic. By iterating this monad starting from the empty $ω$-category, we get a cosimplicial object in strict $ω$-categories. Our main contribution is to show that this cosimplicial object is the cosimplicial objects of orientals. To do so, we prove, using Steiner's theory of augmented directed chain complexes, a general result for comparing polygraphs having same generators and same linearized sources and targets.
