A Generalized Class of T-norms From a Categorical Point of View

Triangular norms or t-norms, in short, and automorphisms are very useful to fuzzy logics in the narrow sense. However, these notions are usually limited to the set [0,1]. In this paper we will consider a generalization of the t-norm notion for arbitrary bounded lattices as a category, where these generalized t-norms are the objects, and a generalization of automorphism notion as the morphism of the category. We will prove that, this category is Cartesian and a subcategory of it is Cartesian closed. We show that the usual interval t-norms can be seen as a covariant functor for that category.