In this paper, for a complete residuated lattice L, we present the categorical properties of-neighborhood spaces and their categorical relationships to neighborhood spaces and stratified L-neighborhood spaces. The main results are: (1) the category of-neighborhood spaces is a topological category; (2) neighborhood spaces can be embedded in-neighborhood spaces as a reflective subcategory, and when L is a meet-continuous complete residuated lattice,-neighborhood spaces can be embedded in stratified L-neighborhood spaces as a reflective subcategory; (3) when L is a continuous complete residuated lattice, neighborhood spaces (resp.,-neighborhood spaces) can be embedded in-neighborhood spaces (resp., stratified L-neighborhood spaces) as a simultaneously reflective and coreflective subcategory