Nonlocal pseudosymmetries and Bäcklund transformations as $\mathcal{C}$-morphisms

In this paper, we show how factorisation with respect to nonlocal pseudosymmetries allows one to obtain Bäcklund transformations, interpreted as nonlocal $\mathcal{C}$-morphisms of differential equations. According to this approach, which is illustrated through several examples, the Bäcklund transformations are determined by basic invariants of the exploited nonlocal pseudosymmetries.