Example 6

Tag 01TD, permanent. Cite it as [Bourbaki, Tag 01TD].

Topologie algébrique, chapter II, § 3. Groupoïdes

Let $\varphi : G\rightarrow G'$ be a morphism of groupoids. The quiver $\varphi (G)$ whose set of vertices is $\varphi$ (Som(G)) and whose set of arrows is $\varphi$ (Fl(G)) is not in general a subgroupoid of $G'$ . This is nevertheless the case if the mapping Som( $\varphi$ ) is injective (II, p. 225, exerc. 5).

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

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