Bourbaki

Exercise 3, § 4

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

Algebraic Topology, I, p. 145

(a) A product of locally trivial fibrations is a locally trivial fibration only if all but a finite number are trivial.

(b) A fibre product of surjective coverings is a covering only if all but a finite number are isomorphisms.

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Machine translation of the English, by gpt-5-mini. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.