Cotorsion torsion triples and the representation theory of filtered hierarchical clustering

Ulrich Bauer; Magnus B. Botnan; Steffen Oppermann; Johan Steen

doi:10.1016/j.aim.2020.107171

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arXiv · 1904.07322

Cotorsion torsion triples and the representation theory of filtered hierarchical clustering

Ulrich Bauer·Magnus B. Botnan·Steffen Oppermann·Johan Steen

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Abstract

We give a full classification of representation types of the subcategories of representations of an $m \times n$ rectangular grid with monomorphisms (dually, epimorphisms) in one or both directions, which appear naturally in the context of clustering as two-parameter persistent homology in degree zero. We show that these subcategories are equivalent to the category of all representations of a smaller grid, modulo a finite number of indecomposables. This equivalence is constructed from a certain cotorsion torsion triple, which is obtained from a tilting subcategory generated by said indecomposables.

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Ulrich Bauer, Magnus B. Botnan, Steffen Oppermann, Johan Steen. 2019-04-15. Cotorsion torsion triples and the representation theory of filtered hierarchical clustering. https://doi.org/10.1016/j.aim.2020.107171

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