A categorical approach to loops neardomains and nearfields

In this paper we study loops, neardomains and nearfields from a
categorical point of view. By choosing the right kind of morphisms, we
can show that the category of neardomains is equivalent to the
category of sharply 2-transitive groups. The other categories are also
shown to be equivalent with categories whose objects are sets of
permutations with suitable extra properties.

Up to now the equivalence between neardomains and sharply 2-transitive
groups was only known when both categories were equipped with the
obvious isomorphisms as morphisms. We thank Hubert Kiechle for this
observation.

Publication year:2012

Keywords:Loops, neardomains, category, morphisms, permutation set