Vinciarelli, Damiano (2018) Torsion theory in Giraud subcategories of the functor category of a ring. [Magistrali biennali]
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In the last years, growing attention has been paid to the employment of the functor categories of a ring to better understand the representation of the ring itself. In this thesis a new aspect is analyzed: it is indeed possible to show that module categories can be embedded as Giraud (co-Giraud) subcategories in their contravariant (covariant) functor categories, and a proof of this fact is given. Also, a focus on the transfer of torsion pairs from the functor category to the underlying module category (and viceversa) is made. Finally, an original proof of the Gabriel-Popescu theorem (as a powerful example of the employment of Giraud subcategories) is given, together with the original proof of some of its corollaries.
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