Subcategories of the category of ⊺-convergence spaces

⊺-convergence structures serve as an important tool to describe fuzzy topology. This paper aims to give further investigations on ⊺-convergence structures. Firstly, several types of ⊺-convergence structures are introduced, including Kent ⊺-convergence structures, ⊺-limit structures and principal ⊺-convergence structures, and their mutual categorical relationships as well as their own categorical properties are studied. Secondly, by changing of the underlying lattice, the “change of base" approach is applied to ⊺-convergence structures and the relationships between ⊺-convergence structures with respect to different underlying lattices are demonstrated.