EXTENSION, RESTRICTION AND PICARD-BRAUER EXACT SEQUENCES FOR TORSION THEORIES

If C, D are Grothendieck categories and F : C --> D, G : D --> C are f unctors satis bing convenient conditions, the extension an restriction of torsion theories preserves the compatibility. Moreover, two idempo tent kernel functors are compatible in D if, and only if, their extens ions are compatible in C. Finally, when C, D are symmetric closed, we obtain relations between erect sequences of Picard and Brauer groups f or the extension and restriction of torsion theories.