# Representability result

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.