Lemma 84.8.4. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. Then there are commutative diagrams of topoi
and
with $a_ X = \pi _ X \circ \epsilon _ X$ and $a_ Y = \pi _ X \circ \epsilon _ X$.
Lemma 84.8.4. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. Then there are commutative diagrams of topoi
and
with $a_ X = \pi _ X \circ \epsilon _ X$ and $a_ Y = \pi _ X \circ \epsilon _ X$.
Proof. This follows immediately from working out the definitions of the morphisms involved, see Topologies on Spaces, Section 73.8 and Section 84.5. $\square$
Your email address will not be published.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).
All contributions are licensed under the GNU Free Documentation License.
Comments (0)