Lemma 64.3.1. Let $S$ be a scheme contained in $\mathit{Sch}_{fppf}$ and let $X$, $Y$ be objects of $(\mathit{Sch}/S)_{fppf}$. Let $f : X \to Y$ be a morphism of schemes. Then

is a representable transformation of functors.

Lemma 64.3.1. Let $S$ be a scheme contained in $\mathit{Sch}_{fppf}$ and let $X$, $Y$ be objects of $(\mathit{Sch}/S)_{fppf}$. Let $f : X \to Y$ be a morphism of schemes. Then

\[ h_ f : h_ X \longrightarrow h_ Y \]

is a representable transformation of functors.

**Proof.**
This is formal and relies only on the fact that the category $(\mathit{Sch}/S)_{fppf}$ has fibre products.
$\square$

Your email address will not be published. Required fields are marked.

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).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.

## Comments (0)

There are also: