Construction 9.4.3.1.2 (00Z8): Construction of the Groupoid Completion of a Category

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Table of Contents
Part 3: Category Theory
Chapter 9: Categories
Section 9.4: Groupoids
Subsection 9.4.3: The Groupoid Completion of a Category
Construction 9.4.3.1.2: Construction of the Groupoid Completion of a Category (cite)

Construction 9.4.3.1.2 ▶ Construction of the Groupoid Completion of a Category

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.)

Proof of Construction 9.4.3.1.2.

Omitted.

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