Given a groupoid G\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {G}$$\end{document} we introduce the category of strict partial groupoid actions of G\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {G}$$\end{document} and state an equivalence between this category and the category of star injective functors to G\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {G}$$\end{document}. Furthermore, fixing a partial action α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha$$\end{document} we give categorical type relations between the action groupoids (G,X)\documentclass[12pt]{minimal}
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\begin{document}$$(\mathcal {G},X)$$\end{document} and (G,XG),\documentclass[12pt]{minimal}
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\begin{document}$$(\mathcal {G}, X_\mathcal {G}),$$\end{document} being XG\documentclass[12pt]{minimal}
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\begin{document}$$X_\mathcal {G}$$\end{document} a universal globalization of X, the coarse groupoid of X and the graph of α\documentclass[12pt]{minimal}
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\begin{document}$$\alpha$$\end{document}. Moreover, when G\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal {G}$$\end{document} is a star open topological groupoid acting partially on a topological space X, we provide conditions for which the partial action is topological and the corresponding quotient map q to XG\documentclass[12pt]{minimal}
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\begin{document}$$X_{\mathcal {G}}$$\end{document} is open. Also, we prove that there is a quotient map XG→Y\documentclass[12pt]{minimal}
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\begin{document}$$X_\mathcal {G}\rightarrow Y$$\end{document}, being Y a topological space endowed with a global action and having X as an open subset.
