Abstract
If C,V are Grothendieck categories and F :C→D,G :D→C are functors satisfying convenient conditions, the extension an restriction of torsion theories preserves the compatibility.Moreover, two idempotent kernel functors are compatible in D if, and only if, their extensions are compatible in C.Finally, when C,D are symmetric closed, we obtain relations between exact sequences of Picard and Brauer groups for the extension and restriction of torsion theories.
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