A categorical approach to loops, neardomains and nearfields. (Q1932145)

The authors state an equivalence between the categories of sharply 2-transitive groups and neardomains. This equivalence was basically known if the morphisms are taken to be isomorphisms. New is the use of injective homomorphisms as morphisms. This reviewer is convinced that the distinction between characteristic~\(2\) or not is unnecessary in the definition of morphisms for sharply 2-transitive groups, as the desired result seems to follow from known properties of the set of involutions. As a warm up the authors construct an -- in essence well-known -- equivalence for loops and regular permutation sets.