Why do mathematicians not talk about $n$-contravariant antisymmetric tensors? (Contravariant $n$-forms)

Question

In every course on differential geometry one is introduced to the concept of vectors ($(1,0)$-tensors), one forms ($(0,1)$-tensors), generic $(m,n)$-tensors and $n$-forms i.e. $(0,n)$-tensors that are totally antisymmetric. It turns out $n$-forms have a rich algebra and can be differentiated and integrated without a metric. The question is, why mathematicians do not talk about $(n,0)$-tensors that are totally antisymmetric? It seems to me one could define a wedge product for these objects completely analogous to the one on forms and maybe one could also define their derivative...would these object be of any interest?