Cyclic theory and the pericyclic category

Autor:	Connes, Alain, Consani, Caterina
Rok vydání:	2022
Předmět:	Mathematics - Algebraic Topology Mathematics - Category Theory Mathematics - Quantum Algebra Primary 55U40 18F10 Secondary 14C40 18B40
Druh dokumentu:	Working Paper
Popis:	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. Comment: 20 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.08339 Zobrazit plný text záznamu View this record from Arxiv