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<p>It is shown that any localisation of triangulated categories induces (up to an equivalence) a localisation of abelian categories when one passes to their abelianisations. From this one obtains for any enlargement of Grothendieck universes an example of an abelian category and a Serre subcategory within the smaller universe such that the corresponding quotient does only exist within the bigger universe. The second part of this note provides an analogue for the abelian hull of an arbitrary category.</p>

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Abelian versus triangulated quotients

  • 期刊论文

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  • 发表日期：

    2025年8月13日

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  • Henning Krause

摘要

It is shown that any localisation of triangulated categories induces (up to an equivalence) a localisation of abelian categories when one passes to their abelianisations. From this one obtains for any enlargement of Grothendieck universes an example of an abelian category and a Serre subcategory within the smaller universe such that the corresponding quotient does only exist within the bigger universe. The second part of this note provides an analogue for the abelian hull of an arbitrary category.