A normalized \(T\)-monoid \((X : X_0 \nrightarrow TX_0, u, m)\) for a monad \(T\) on a virtual double category \(\mathbb {X}\) is unwirable iff its composition cell is cartesian in \(\mathbb {X}\).
That is, every cell with boundaries as on the left, factors uniquely through the composition cell \(m\) as on the right,
