  Skew braces are algebraic structures related to the solutions of the
set-theoretic quantum Yang-Baxter equation. We develop the central nilpotency
theory for such algebraic structures in the sense of Freese-McKenzie
\cite{comm} and we compare the universal algebraic notion of central nilpotency
with the notion of right and left $*$-nilpotency developed in
\cite{NilpotentType}.
