Lemma 1

Tag 05PS, permanent. Cite it as [Bourbaki, Tag 05PS].

For every homomorphism $u : F \to F'$ , the diagram

\begin{array}{ccc} T(F) & \xrightarrow{\nu_F} & T'(F) \\ \downarrow T(u) & & \downarrow T'(u) \\ T(F') & \xrightarrow{\nu_{F'}} & T'(F') \end{array}

is commutative.

The verification is immediate.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.