Flat covers and injective hulls of persistence modules

Eero Hyry; Ville Puuska

doi:10.1016/j.jpaa.2025.107874

Flat covers and injective hulls of persistence modules

Eero Hyry^*
, Ville Puuska

^*Corresponding author for this work

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Abstract

Motivated by recent progress in topological data analysis, we establish a Matlis duality between injective hulls and flat covers of persistence modules. This extends to a duality between minimal flat and minimal injective resolutions. We utilize the theory of flat cotorsion modules and flat covers developed by Enochs and Xu. By means of this theory we can work with persistence modules which are not tame or even pointwise finite-dimensional.

Original language	English
Article number	107874
Journal	Journal of Pure and Applied Algebra
Volume	229
Issue number	2
DOIs	https://doi.org/10.1016/j.jpaa.2025.107874
Publication status	Published - 2025
Publication type	A1 Journal article-refereed

Keywords

Cotorsion
Flat cover
Injective hull
Matlis dual
Multiparameter persistence module

Publication forum classification

Publication forum level 1

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2025.107874Licence: CC BY

Flat covers and injective hulls of persistence modulesFinal published version, 543 KBLicence: CC BY

https://urn.fi/URN:NBN:fi:tuni-202501311858Licence: CC BY

Cite this

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abstract = "Motivated by recent progress in topological data analysis, we establish a Matlis duality between injective hulls and flat covers of persistence modules. This extends to a duality between minimal flat and minimal injective resolutions. We utilize the theory of flat cotorsion modules and flat covers developed by Enochs and Xu. By means of this theory we can work with persistence modules which are not tame or even pointwise finite-dimensional.",

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AU - Puuska, Ville

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AB - Motivated by recent progress in topological data analysis, we establish a Matlis duality between injective hulls and flat covers of persistence modules. This extends to a duality between minimal flat and minimal injective resolutions. We utilize the theory of flat cotorsion modules and flat covers developed by Enochs and Xu. By means of this theory we can work with persistence modules which are not tame or even pointwise finite-dimensional.

KW - Cotorsion

KW - Flat cover

KW - Injective hull

KW - Matlis dual

KW - Multiparameter persistence module

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DO - 10.1016/j.jpaa.2025.107874

M3 - Article

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Flat covers and injective hulls of persistence modules

Abstract

Keywords

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ASJC Scopus subject areas

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