Proposition 9

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

Let $E', E, E''$ be A-modules and

E' \xrightarrow{u} E \xrightarrow{v} E'' \longrightarrow 0

an exact sequence of linear mappings. Then the sequence of transpose mappings

0 \longrightarrow {E''}^* \xrightarrow{{}^t v} E^* \xrightarrow{{}^t u} {E'}^*

is exact.

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

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