Length 3 complexes of abelian sheaves and Picard 2-stacks

A. Emin Tatar

We define a tricategory $T^{[-2,0]}$ of length 3 complexes of abelian sheaves, whose hom-bigroupoids consist of weak morphisms of such complexes. We also define a 3-category 2Pic(S) of Picard 2-stacks, whose hom-2-groupoids consist of additive 2-functors. We prove that these categories are triequivalent as tricategories. As a consequence we obtain a generalization of Deligne's analogous result about Picard stacks in SGA4, Expose' XVIII.