Notes on weak units of Picard 1- and 2-stacks
Ettore Aldrovandi, Ahmet Emin Tatar
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.