Link and knot invariants from non-abelian Yang-Baxter 2-cocycles

We define a knot/link invariant using set theoretical solutions $(X,\sigma )$ of the Yang-Baxter equation and non commutative 2-cocycles. We also define, for a given $(X,\sigma )$, a universal group Unc(X) governing all 2-cocycles in $X$, and we exhibit examples of computations.