A categorical approach to loops, neardomains and nearfields

作者：Cara Philippe^*; Kieboom Rudger; Vervloet Tina

来源：Bulletin of the Belgian Mathematical Society Simon Stevin, 2012, 19(5): 845-857.

• Equivalence of categories
• Loops
• Neardomains
• Sharply 2-transitive groups

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. %26lt;br%26gt;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 [6].

• 出版日期2012