  We show that the definition of unrolled Hopf algebras can be naturally
extended to the Nichols algebra $\mathcal{B}$ of a Yetter-Drinfeld module $V$
on which a Lie algebra $\mathfrak g$ acts by biderivations. Specializing to
Nichols algebras of diagonal type, we find unrolled versions of the small, the
De Concini-Procesi and the Lusztig divided power quantum group, respectively.
