In [1] the authors proposed a generalization of the notion of homotopy, a relation called to be box-homotopic, proven to be an equivalence relation on $Top(X,Y)$ and well-adjusted with the composition. In this article we prove that all the mappings of $Top(X,Y)$ are box-homotopic, that is, the classification of morphisms by the box-homotopy relation is the coarsest.
| On classification of morphisms by box-homotopy | 478.9KB |