Aspects of the category SKB of skew braces

We examine the pointed protomodular category SKB of left skew braces. We study the notion of commutator of ideals in a left skew brace. Notice that in the literature, “product” of ideals of skew braces is often considered. We show that the so-called (Huq = Smith) condition holds for left skew braces. Finally, we give a set of generators for the commutator of two ideals, and prove that every ideal of a left skew brace has a centralizer.