Corollary 1

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

Algebra, chapter II, § 1. Modules

Let $T, T'$ be two sets, $g : T \to T'$ a mapping. Then there exists one and only one A-linear mapping $f : A^{(T)} \to A^{(T')}$ which renders commutative the diagram

\begin{array}{ccc} T & \overset{g}{\longrightarrow} & T' \\ \downarrow \phi & & \downarrow \phi' \\ A^{(T)} & \overset{f}{\longrightarrow} & A^{(T')} \end{array}

where $\phi$ and $\phi'$ are the canonical mappings.

It suffices to apply Proposition 17 to the composite mapping $T \overset{g}{\to} T' \overset{\phi'}{\to} A^{(T')}$ .

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

Cited by

Nothing.

Cites

Proposition 17