I'm looking for references regarding an unpublished Deligne's manuscript "Une descrption de catégorie tressée (inspiré par Drinfeld)" and the subject it touches, that is described in the post title. If it's not available online maybe someone can orient me to some other references regarding the same connection or to the connection itself for me to try to develop the details.


Thanks,



Connection between braided tensor categories and local systems on moduli of stable marked genus zero curves
Welcome to MO.
One place where this idea is somewhat explained is Bezrukavnikov-Finkelberg- Schechtman, Factorizable sheaves and quantum groups (<https://arxiv.org/abs/q-alg/9712001>) but maybe this is where you heard about it.


I'd say nowadays this idea might be best understood as a particular case of the identifications between:


* braided monoidal categories, and algebras over the little disks operad in Cat
* algebras over the little disks operad and locally constant factorization algebras on $\mathbb{R}^2$.


