On generalized sharply $n$-transitive groups

We regard generalized sharply $n$-transitive groups as generalizations of affine, projective, $n$-transitive transformation groups. Pseudo-fields of degree $n$ are regarded as generalizations of the algebraic systems of near-domains, $\mathrm{KT}$-fields and fields of degree $n$. We prove that generalized sharply $n$-transitive groups and pseudo-fields of degree $n$ are category equivalent.