Definition 2
Tag 01T0, permanent. Cite it as [Bourbaki, Tag 01T0].
Topologie algébrique, chapter II, § 3. Groupoïdes
A category is a quiver endowed with an associative law of composition for which there exists at each vertex an identity element.
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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