论文标题
环状理论和周环类别
Cyclic theory and the pericyclic category
论文作者
论文摘要
我们对循环类别在循环理论的发展中的作用给出了历史观点。这涉及到特征性一体的扩展，S-Elgebras的扩展，传统的环状理论发展以及与涉及几个小类别相关的座椅的几何形状。我们阐明了环状的各种现有演示文稿与环保类别之间的联系，并通过将整数的环作为3的多项式呈现为多项式，并在球形组环中的系数[C_2]中的系数示出了绝对系数的作用。最后，我们介绍了周期性类别，该类别统一并完善了文献中存在的两个环保空间的矛盾概念。
We give a historical perspective on the role of the cyclic category in the development of cyclic theory. This involves a continuous interplay between the extension in characteristic one and in S-algebras, of the traditional development of cyclic theory, and the geometry of the toposes associated with several small categories involved. We clarify the link between various existing presentations of the cyclic and the epicyclic categories and we exemplify the role of the absolute coefficients by presenting the ring of the integers as polynomials in powers of 3, with coefficients in the spherical group ring S[C_2] of the cyclic group of order two. Finally, we introduce the pericyclic category which unifies and refines two conflicting notions of epicyclic space existing in the literature.
