A vector field is a pointwise assignment of vectors(arrows).
Tensors are defined as $\mathbb{R}$-valued multilinear maps, and a tensor field is a pointwise assignment of tensors.
Also, a vector space $V$ is isomorphic to it's dual space $V^*$(thus, a vector can be realized as a linear operator too).
Is a tensor a generalization of a vector in the sense that a tensor is a multilinear map, and a vector can be seen as an operator(since V $\cong$ V*)? And thus, vector fields are just assignments of '1-tensors', and differential forms assignments of 'k-tensors'?