Cotorsion torsion triples and the representation theory of filtered hierarchical clustering

Ulrich Bauer*, Magnus B. Botnan, Steffen Oppermann, Johan Steen

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


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.

Original languageEnglish
Article number107171
Pages (from-to)1-51
Number of pages51
JournalAdvances in Mathematics
Early online date27 Apr 2020
Publication statusPublished - 5 Aug 2020


  • Hierarchical clustering
  • Multiparameter persistence
  • Quiver representation theory
  • Torsion theory


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