On the isomorphy of categories of probabilistic limit spaces under t-norms

We show that for the classes of strict t-norms, the categories of probabilistic limit spaces under these t-norms are all isomorphic to eachother. The same is true for the categories of probabilistic limit spacesunder nilpotent t-norms. To show this, we study the isomorphisms be-tween the categories of probabilistic limit spaces under a t-norm, limittower spaces and approach limit spaces. Similar results are obtainedfor probabilistic Cauchy spaces and probabilistic uniform limit spaces.&nbsp