THE GROUP OF STRONG GALOIS OBJECTS ASSOCIATED TO A COCOMMUTATIVE HOPF QUASIGROUP
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Let $H$ be a cocommutative faithfully flat Hopf quasigroup in a strict symmetricmonoidal category with equalizers. In this paper we introduce the notion of (strong) Galois $H$-object and we prove that the set of isomorphism classes of (strong) Galois $H$-objects is a (group) monoid which coincides, in the Hopf algebra setting, with the Galois group of $H$-Galois objects introduced by Chase and Sweedler.
Abstract
Let $H$ be a cocommutative faithfully flat Hopf quasigroup in a strict symmetricmonoidal category with equalizers. In this paper we introduce the notion of (strong) Galois $H$-object and we prove that the set of isomorphism classes of (strong) Galois $H$-objects is a (group) monoid which coincides, in the Hopf algebra setting, with the Galois group of $H$-Galois objects introduced by Chase and Sweedler.
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