Length 3 Complexes of Abelian Sheaves and Picard 2-Stacks
Algebraic Geometry
2014-01-29 v2 Category Theory
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.
Keywords
Cite
@article{arxiv.0906.2393,
title = {Length 3 Complexes of Abelian Sheaves and Picard 2-Stacks},
author = {A. Emin Tatar},
journal= {arXiv preprint arXiv:0906.2393},
year = {2014}
}
Comments
46 pages, the proof of proposition 6.2 is added as appendix