Nearness spaces were defined for the goal of unifying several types of topological structures by H. Herrlich. The basic motivation of the theory of textures is to find a convenient point set based setting for fuzzy sets. This is the second of three papers which develop various fundamental aspects of the concept of dinearness texture spaces in a categorical setting and present important links with the theory of nearness spaces. Further, it is proved that the category extbf{Near} of nearness spaces is to isomorphic to the full subcategory of dinearness texture spaces.