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Mar 13, 2017 at 12:12 comment added Mike Shulman In any topos, the subobject classifier is internally injective, so that any injection $A\rightarrowtail B$ yields a surjection $\Omega^B \twoheadrightarrow\Omega^A$. Thus, an injection $\Omega^Y \rightarrowtail Y$ gives a surjection $\Omega^Y \to \Omega^{\Omega^Y}$, allowing us to apply Cantor's theorem.
Mar 12, 2017 at 20:30 history answered Qiaochu Yuan CC BY-SA 3.0