Proposition 6

Tag 05R5, permanent. Cite it as [Bourbaki, Tag 05R5].

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

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

d_F : \operatorname{Hom}_A(\lim \overrightarrow{E_\alpha}, F) \to \lim \leftarrow \operatorname{Hom}_A(E_\alpha, F).

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

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Cites

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