It is all in the title.
find an example of a fibration $p:\mathcal{C}\to\mathcal{B}$, so that $p$ has fibred product, but $\mathcal{C}$ doesn't have product
2026-05-06 02:21:08.1778034068
Example of a Grothendieck fibration has fibred product (or other universal structure) but total category doesn't has product?
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Just take the codomain fibration defined with respect to a category with pullbacks but without binary products. An example of such a category is the category with objects sets and injective maps as morphisms. – Nex 52 mins ago