Geodesic
Generalized persistence and graded structures
Homology, homotopy, and applications, Tome 24 (2022) no. 1, pp. 27-53.

Voir la notice de l'article provenant de la source International Press of Boston

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.
DOI : 10.4310/HHA.2022.v24.n1.a2
Classification : 13E15, 16D90, 16W50
Keywords: persistence module, graded module, action category, smash product, finitely presented 
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Eero Hyry; Markus Klemetti. Generalized persistence and graded structures. Homology, homotopy, and applications, Tome 24 (2022) no. 1, pp. 27-53. doi : 10.4310/HHA.2022.v24.n1.a2. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n1.a2/

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