Gabriel-Popescu type theorems and applications |
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Authors: | F Castañ o Iglesias,P Enache,B Torrecillas |
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Abstract: | In this paper we obtain a general version of Gabriel-Popescu theorem representing any Grothendieck category as a quotient category of the category of modules over a ring (not necessarily with unit) with enough idempotents to right using a family of generators (Ui)i∈I of where Ui are not supposed to be small. Applications to locally finite categories are obtained. In particular, for a coalgebra C (over a field) we prove that C is right semiperfect if and only if the category has the AB4∗ condition. |
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Keywords: | 16D90 18E15 16W30 |
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