Augmentations are sheaves for Legendrian graphs (Q2112638)

In this paper, the authors show and study the equivalence between two categorical Legendrian isotopy invariants: the augmentation category and a DG category of constructible sheaves. First, they give some prelimiaries. Then they define augmentation categories for bordered Legendrien graphs. The main result is then obtained: the authors prove that augmentations are sheaves for Legendrian graphs. The details of the proof are given.