Concretely, the groupoid completion of $\mathcal{C}$ is the Gabriel–Zisman localisation $\textup{Mor}\webleft (\mathcal{C}\webright )^{-1}\mathcal{C}$ of $\mathcal{C}$ at the set $\textup{Mor}\webleft (\mathcal{C}\webright )$ of all morphisms of $\mathcal{C}$; see .

(To be expanded upon later on.)

Omitted.


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