| In SGA4, Deligne proves that to any strictly picard stack one can associate a complex of abelian sheaves of length 2. He also studies the morphisms between such stacks and shows that such a morphism defines a class of fractions in the derived category of complexes of abelian sheaves. In this talk, I will first define derived categories and stacks and discuss Deligne's theorem. I will also provide a brief introduction to the terminology of 2-categories, 2-stacks, and some structures on them. Then I will talk about my thesis where I generalized Deligne's theorem to the case of strictly Picard 2-stacks so that Deligne's theorem becomes a corollary of my work. |