We prove in this paper that the category HM whose objects are topological spaces and whose morphisms are homotopy classes of multi-nets is naturally equivalent to the shape category Sh. The description of the category HM was given earlier in the article "Shape via multi-nets". We have shown there that HM is naturally equivalent to Sh only on a rather restricted class of spaces. This class includes all compact metric spaces where a similar intrinsic description of the shape category using multi-valued functions was given by José M. R. Sanjurjo in [5] and [6].