On the connection between Hopf–Galois structures and skew braces

We present a different version of the well-known connection between Hopf–Galois structures and skew braces, building on recent paper A. Koch P. J. Truman. show that known results involve this easily carry over to new perspective, ones naturally appear. As an application, we insights study surjectivity correspondence, explaining in more detail role bi-skew braces theory.