In my preprint I defined pre-order of pointfree funcoids by the formula $latex f\sqsubseteq g \Leftrightarrow [f]\subseteq[g]$. Sadly this does not define a poset, but only a pre-order.

Recently I’ve found an other (non-equivalent) definition of an order on pointfree funcoids, this time this is a partial order not just a pre-order:

$latex f \sqsubseteq g \Leftrightarrow \forall x \in \mathfrak{A}: \langle f \rangle

x \sqsubseteq \langle g \rangle x \wedge \forall y \in \mathfrak{B}: \langle

f^{- 1} \rangle y \sqsubseteq \langle g^{- 1} \rangle y$.

x \sqsubseteq \langle g \rangle x \wedge \forall y \in \mathfrak{B}: \langle

f^{- 1} \rangle y \sqsubseteq \langle g^{- 1} \rangle y$.

I will systematically rewrite the relevant chapters of my manuscript to replace the old definition with the new one.

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