Applying (0x66d95e87) we also may identify a smooth tensor field \(\Gamma(T^{(k+1,l)}TM)\) with a \(C^\infty(M)\)-multilinear map
\begin{equation*} F\colon \underbrace{\mathcal{T}^1\times \cdots \times \mathcal{T}^1}_\text{\(k\) factors} \times \underbrace{\mathfrak{X}(M)\times \cdots \times \mathfrak{X}(M)}_\text{\(l\) factors} \to \mathfrak{X}(M), \end{equation*}