It seems to me that Picard stacks as defined by Deligne and used in algebraic geometry are stacks of symmetric monoidal categories. Am I missing something? Is there a difference between the two notions? The Picard stack I am interested in shows up in symplectic toric geometry (arXiv:0908.2783v2[math.SG] )

objectsare invertible (with respect to the monoidal structure). – Konrad Waldorf Jul 26 '12 at 18:43