The Grothendieck group of an n-angulated category

• Autores: Petter Andreas Bergh, Marius Thaule
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 218, Nº 2, 2014, págs. 354-366
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2013.06.007
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• Resumen

  • We define the Grothendieck group of an n-angulated category and show that for odd n its properties are as in the special case of n = 3, i.e. the triangulated case. In particular, its subgroups classify the dense and complete n-angulated subcategories via a bijective correspondence.

    For a tensor n-angulated category, the Grothendieck group becomes a ring, whose ideals classify the dense and complete n-angulated tensor ideals of the category.