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A categorical approach to loops, neardomains and nearfields. (English) Zbl 1279.20002

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.

MSC:

20B22 Multiply transitive infinite groups
20N05 Loops, quasigroups
12K05 Near-fields
18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms
16D90 Module categories in associative algebras
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