As the title says. Let's consider some category $C$ and the contravariant functor $Sub : C^{op} \rightarrow Set$ that for each object gives its set of subobjects. The introductory book by Leinster says that by the Yoneda lemma, $Sub$ being representable amounts to there being an object $\Omega$ a...

As the title says. Let's consider some category $C$ and the contravariant functor $Sub : C^{op} \rightarrow Set$ that for each object gives its set of subobjects. The introductory book by Leinster says that by the Yoneda lemma, $Sub$ being representable amounts to there being an object $\Omega$ a...