Generalized persistence and graded structures

Autor:	Hyry, Eero, Klemetti, Markus
Rok vydání:	2021
Předmět:	Mathematics - Algebraic Topology 16D90 (Primary) 13E15 16W50 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We investigate the correspondence between generalized persistence modules and graded modules in the case the indexing set has a monoid action. We introduce the notion of an action category over a monoid graded ring. We show that the category of additive functors from this category to the category of Abelian groups is isomorphic to the category of modules graded over the set with a monoid action, and to the category of unital modules over a certain smash product. Furthermore, when the indexing set is a poset, we provide a new characterization for a generalized persistence module being finitely presented. Comment: 25 pages, to appear in Homology, Homotopy and Applications
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2102.06577 Zobrazit plný text záznamu View this record from Arxiv