Extensional L-fuzzy Q-convergence structures

In this paper, the concept of extensional L-fuzzy Q-convergence structures is proposed. It is shown that there is an adjunction between the category of extensional L-fuzzy topological spaces and the category of extensional L-fuzzy topological spaces. In particular, the category of extensional L-fuzzy topological spaces can be embedded in the category of extensional L-fuzzy Q-convergence spaces as a reflective subcategory. Also, the notion of topological extensional L-fuzzy Q-convergence spaces is introduced and the resulting category is shown to be isomorphic to the category of extensional L-fuzzy topological spaces.