Abstract
We consider the category of partial actions, where the group and the set upon which the group acts can vary. Within this framework, we develop a theory of quotient partial actions and prove that this category is both (co)complete and encompasses the category of groupoids as a full subcategory. In particular, we establish the existence of a pair of adjoint functors, denoted as Φ : Grpd → PA and Ψ : PA → Grpd , with the property that Ψ Φ ≅ 1 Grpd . Next, for a given groupoid Γ, we provide a characterization of all partial actions that allow the recovery of the groupoid Γ through Ψ . This characterization is expressed in terms of certain normal subgroups of a universal group constructed from Γ .
Published Version
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