T-convergence structures serve as an important tool to describe fuzzy topology and deserve more and more attention. This paper aims to give further investigations onT-convergence structures. Firstly, several types of $\top$-convergence structures are introduced, including Kent T-convergence structures, T-limit structures and principal T-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 T-convergence structures and the relationships between T-convergence structures with respect to different underlying lattices are demonstrated.