Strong L-concave structures and L-convergence structures

Considering a complete residuated lattice L as the truth-value table, we propose concepts of strong L-concave structures and idempotent L-concave interior operators, and show that they are one-to-one corresponding. Also we introduce the notion of (concave) L-convergence structures and prove that the category of strong L-concave spaces can be embedded in the category of L-convergence spaces as a reflective subcategory.