Let $X$ and $S$ be schemes over a field $k$.

Reading this paper, there is a result on the representability of a morphism (proposition 3.1, page 4).

Which result or reference on representability is used in this proposition?

The forgetful morphism $ {\mathcal C(r, X)\to\mathcal M(r,X) \times \Bbb A^1} $ is representable.

Where $\mathcal C(r,X)$ is a stack over $ \operatorname{\textbf{Aff}} /\Bbb A^1 $ with objects the vector bundles on $X\times_k S$, and $ \mathcal M(r,X) $ is the stack of rank-$ r $ vector bundles of degree zero on $ X $.

The authors seem to construct an $S$-category of triples(which reminds me of a $2$-fiber product) and prove that it is represented by a geometric object but I don't see which theorems or definition they're using.

Many Thanks for any insights or references.



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