Lemma 84.3.4. In Situation 84.3.3 there is an equivalence of categories between

$\mathop{\mathit{Sh}}\nolimits (\mathcal{C}_{total})$, and

the category of systems $(\mathcal{F}_ n, \mathcal{F}(\varphi ))$ described above.

In particular, the topos $\mathop{\mathit{Sh}}\nolimits (\mathcal{C}_{total})$ only depends on the topoi $\mathop{\mathit{Sh}}\nolimits (\mathcal{C}_ n)$ and the morphisms of topoi $f_\varphi $.

## Comments (0)

There are also: