Cotorsion torsion triples and the representation theory of filtered hierarchical clustering

By Ulrich Bauer, Magnus Bakke Botnan, Steffen Oppermann, Johan Steen. Advances in Mathematics, 2019

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Abstract We give a full classification of representation types of the subcategories of representations of an m × 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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/610900fe23745f6018f7ac4a2be41b74bf406936