A new theorem and a conjecture

I’ve just proved the following:

Theorem (\mathsf{FCD}) (\mathsf{RLD})_{\Gamma} f = f for every funcoid f.

For a proof see this online article.

I’ve also posed the conjecture:

Conjecture (\mathsf{FCD}) : \mathsf{RLD} (A ; B) \rightarrow \mathsf{FCD} (A ; B) is the upper adjoint of (\mathsf{RLD})_{\Gamma} : \mathsf{FCD} (A ; B) \rightarrow \mathsf{RLD} (A ; B) for every sets A, B.

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