So this means that the extended reals are the fixed points of the Isbell adjunction between presheaves on Q and copresheaves on Q? Thank you

]]>the extended real line is in fact the *reflexive completion* of Q, as in the category of fixed points of the isbell duality adjunction (here, that means downward-closed subsets which are fixed by taking their set of upper bounds and then the set of lower bounds of that again)

]]>That sounds right, I’ll edit the example, thanks!

]]>Yep.

]]>Yeah, minor nit, I guess. Also, when you say Hom(-,x) is a representable presheaf, that just means it’s isomorphic to a hom-functor, a trivial fact in this case since it *is* a hom-functor?

]]>Whoops! Yes, I meant “objects”.

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