Length 3 Complexes of Abelian Sheaves and Picard 2-Stacks

Abstract

We define a tricategory T 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, Exp. XVIII.

46 pages, the proof of proposition 6.2 is added as appendix

References in corpus (5)

• Butterflies I: morphisms of 2-group stacks
• On weak maps between 2-groups
• Length 3 Complexes of Abelian Sheaves and Picard 2-Stacks
• 2-Gerbes bound by complexes of gr-stacks, and cohomology
• Bicat is not triequivalent to Gray

Cited by in corpus (3)

• Length 3 Complexes of Abelian Sheaves and Picard 2-Stacks
• Extensions of Picard 2-Stacks and the cohomology groups Ext^i of length 3 complexes
• Higher-dimensional study of extensions via torsors