Remark 1

Tag 03VA, permanent. Cite it as [Bourbaki, Tag 03VA].

Theory of Sets, chapter IV, § 1. Structures and isomorphisms

In applications it is often the case (as in Example 4 above) that the echelon $S(E_1, \ldots, E_n, A_1, \ldots, A_m)$ is a product of echelons

S_1(E_1, \ldots, A_m) \times \cdots \times S_p(E_1, \ldots, A_m).

If so, the letter $s$ in the definition of $\Sigma$ is often replaced by a " $p$ -tuple" $(s_1, \ldots, s_p)$ (cf. Chapter II, § 2, no. 1).

Moreover, the axiom of a species of structures $\Sigma$ is most frequently written as a conjunction of several transportable relations (as in Example 3 above). These relations are called the axioms of the species $\Sigma$ .

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.

Cited by

Nothing.

Cites

Chapter II, § 2, no. 1
Example 3
Example 4