Codistinguished abelian subcategories

Abstract

We introduce codistinguished abelian subcategories of triangulated categories, which generalise Jorgensen's proper abelian subcategories and are dual to Linckelmann's distinguished abelian subcategories. We show that they come equipped with a non-trivial exact structure induced by the ambient triangulated category, and that every exact structure on an abelian category arises in this way. We also show that fully faithful adjunction triples produce new codistinguished abelian subcategories from old.