Proposition 2

Tag 01O6, permanent. Cite it as [Bourbaki, Tag 01O6].

Topologie algébrique, chapter I, § 3. Faisceaux

The mapping $j_{\mathscr{F}}$ is the inverse B-isomorphism of $e_{\mathscr{F}}$ .

For $U\in \mathscr{B},s\in \mathscr{F}(U)$ and $x\in U$ , one has by definition of $j_{\mathscr{F}}:$

j_{\mathscr{F}}([U, s, x]) = [U, \sigma_{\mathscr{F}}(U, s), x]

whence $e_{\mathscr{F}}(j_{\mathscr{F}}([U, s, x])) =\sigma_{\mathscr{F}}(U, s)(x) = [U, s, x]$ . This proves the proposition.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

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