Let $\mathcal{C}$ be a category that has a subobject classifier $\Omega$ (I do not require $\mathcal{C}$ to be a topos).
Does the Yoneda embedding of $\mathcal{C}$ to the presheaf topos on $\mathcal{C}$ preserve the subobject classifier?
2026-03-29 08:56:06.1774774566
Does Yoneda preserve the subobject classifier, if it exists?
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