A normalized \(T\)-monoid \((X : X_0 \nrightarrow TX_0, u, m)\) for a monad \(T\) on a virtual double category \(\mathbb {X}\), i.e. a generalized multicategory or \(T\)-category, is malleable (or unwirable) if and only if 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,
