Lemma 8.8.3. Notation and assumptions as in Lemma 8.8.2. There is a canonical equivalence of categories

$\mathop{Mor}\nolimits _{\textit{Fib}/\mathcal{C}}(\mathcal{S}, \mathcal{X}) = \mathop{Mor}\nolimits _{\textit{Stacks}/\mathcal{C}}(\mathcal{S}', \mathcal{X})$

given by the constructions in the proof of the aforementioned lemma.

Proof. Omitted. $\square$

There are also:

• 7 comment(s) on Section 8.8: Stackification of fibred categories

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).