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A generalization of the Gabriel–Popescu theorem

2004; Elsevier BV; Volume: 190; Issue: 1-3 Linguagem: Inglês

10.1016/j.jpaa.2003.11.016

1873-1376

W. Lowen,

Algebraic structures and combinatorial models

In this paper we give necessary and sufficient conditions for an additive functor u:u→C, from a small pre-additive category u to a Grothendieck category C, to realize C as a localization of the category of presheaves on u. This is a generalization of the Gabriel–Popescu theorem, which considers the case where u is fully faithful.