  The interplay between set-theoretic solutions of the Yang-Baxter equation of
Mathematical Physics, skew braces, regular subgroups, and Hopf Galois
structures has spawned a considerable body of literature in recent years.
  In a recent paper, Alan Koch has generalised a construction of Lindsay N.
Childs, showing how one can obtain bi-skew braces $(G, \cdot, \circ)$ from an
endomorphism of a group $(G, \cdot)$ whose image is abelian.
  In this paper, we first characterise the endomorphisms of a group $(G,
\cdot)$ for which Koch's construction, and a variation on it, yield (bi-)skew
braces. We show how the set-theoretic solutions of the Yang-Baxter equation
derived by Koch's construction carry over to our more general situation, and
discuss the related Hopf Galois structures.
  In a subsequent paper, Koch has shown how to construct brace blocks. This
means that, starting with a group $(G, \cdot)$ and an endomorphism $\psi$ of
$(G, \cdot)$ whose image is abelian, one obtains a set of group operations on a
set $G$, such that under any two of them $G$ becomes a skew brace. We
generalise Koch's work by relaxing the condition on $\psi$, and by allowing
polynomials on $\psi$ in the construction.
