Orientals 作为自由代数
Orientals as free algebras
AI总结：
本文基于 Burroni 思想，通过定义严格 ω-范畴上的扩张并证明其遗忘函子是单子的，从空范畴迭代单子构造出余单纯对象，并利用 Steiner 理论证明该对象即为 Street 的 orientals 余单纯对象。
摘要：
本文旨在给出 Street 的 orientals 余单纯对象的另一种构造，基于 Burroni 的思想，即 orientals 是严格 ω-范畴上某种代数结构的自由代数。更准确地说，遵循 Burroni，我们定义了 ω-范畴上的扩张概念，并证明从赋予扩张的严格 ω-范畴到严格 ω-范畴的遗忘函子是单子的。通过从空 ω-范畴开始迭代此单子，我们得到严格 ω-范畴中的余单纯对象。我们的主要贡献是证明此余单纯对象即 orientals 的余单纯对象。为此，我们利用 Steiner 的增广有向链复形理论，证明了一个用于比较具有相同生成元及线性化源与靶的 polygraphs 的一般性结果。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
