Proposition 2

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

Algebra, chapter II, § 6. Inverse and direct limits of modules

For every inverse system $(E_\alpha, f_{\alpha \beta})$ of $A$ -modules and every $A$ -module $F$ , the canonical mapping $u \mapsto (f_\alpha \circ u)$ is a $\mathbf{Z}$ -module isomorphism

(2)

l_F: \operatorname{Hom}_A(F, \lim_{\leftarrow} E_\alpha) \to \lim_{\leftarrow} \operatorname{Hom}_A(F, E_\alpha).

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

Cited by

§ 6. Inverse and direct limits of modules

Cites

Nothing.