Gabriel–Popescu theorem

In mathematics, the Gabriel–Popescu theorem is an embedding theorem for certain abelian categories, introduced by Pierre Gabriel and Nicolae Popescu (1964). It characterizes certain abelian categories (the Grothendieck categories) as quotients of module categories.

There are several generalizations and variations of the Gabriel–Popescu theorem, given by Kuhn (1994) (for an AB5 category with a set of generators), Lowen (2004), Porta (2010) (for triangulated categories).