Notes on Weak Units of Picard 1- and 2-Stacks

Details Notes on Weak Units of Picard 1- and 2-Stacks Notes on Weak Units of Picard 1- and 2-Stacks

2011-08-09

arxiv.org/abs/1108.1922v2

Mathematics

Algebraic Geometry

17 pages, the complex in Remark 5.4 and the complex in Section 5.5 are revised

Scientific paper

The weak units of strict monoidal 1- and 2-categories have been defined. In this paper, we recall them for Picard 1- and 2-stacks. We show that they form a Picard 1- and 2-stack, respectively. We deduce by characterization theorem for Picard 2-stacks that there exists a length 2 (resp. 3) complex of abelian sheaves that represent the Picard stack (resp. Picard 2-stack) of the weak units. Lastly, we calculate such complexes.

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