On direct product, semidirect product of groupoids and partial actions

We present some constructions of groupoids as: direct product, semidirect product, and we give necessary and sufficient conditions for a groupoid to be embedded into a direct product of groupoids. Also, we establish necessary and sufficient conditions to determine when a semidirect product is direct. Moreover, we establish an equivalence between the category of strict partial groupoid actions and the category of star injective functors. Finally, we give a relation of categorical type between the actions groupoids (G, X) and (G, Y), being Y a universal globalization of X.

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