Stratified L-uniform convergence spaces

We define a supercategory of the category of stratified L-uniform spaces, where L is a complete Heyting algebra. Our category is topological over SET and cartesian closed. In the case where L is the two-point chain, it coincides with the category of uniform convergence spaces. Moreover, we describe the induced stratified L-convergence and show that in case of a stratified L-uniform space this L-convergence is a stratified L-topology.