Triangulated subcategories of extensions, stable t-structures, and triangles of recollements

• Peter Jørgensen ^[2] ; Kiriko Kato ^[1]
  1. [1] Osaka Prefecture University

     Osaka Prefecture University

     Sakai Ku, Japón

     
  2. [2] Newcastle University

     Newcastle University

     Reino Unido

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 12 (December 2015), 2015, págs. 5500-5510
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2015.05.029
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• Resumen

  • In a triangulated category T with a pair of triangulated subcategories X and Y, one may consider the subcategory of extensions X⁎Y.

    We give conditions for X⁎Y to be triangulated and use them to provide tools for constructing stable t-structures. In particular, we show how to construct so-called triangles of recollements, that is, triples of stable t-structures of the form (X,Y), (Y,Z), (Z,X). We easily recover some triangles of recollements known from the literature.