On monads of exact reflective localizations of Abelian categories
classification
🧮 math.CT
keywords
gabrielmonadsabeliancategoriescoimageexactlocalizationsmonad
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In this paper we define Gabriel monads as the idempotent monads associated to exact reflective localizations in Abelian categories and characterize them by a simple set of properties. The coimage of a Gabriel monad is a Serre quotient category. The Gabriel monad induces an equivalence between its coimage and its image, the localizing subcategory of local objects.
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