The Stacks project

Example 76.3.3. It is no longer true that universally injective is equivalent to radicial. For example the morphism

\[ X = [\mathop{\mathrm{Spec}}(\overline{\mathbf{Q}})/ \text{Gal}(\overline{\mathbf{Q}}/\mathbf{Q})] \longrightarrow S = \mathop{\mathrm{Spec}}(\mathbf{Q}) \]

of Spaces, Example 65.14.7 is universally injective, but is not radicial in the sense above.

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View Example 76.3.3 as pdf