A categorical isomorphism between injective balanced L-S0-convex spaces and fuzzy frames

The main purpose of this paper is to show that injective balanced L- S 0 -convex spaces and fuzzy frames are isomorphic from the categorical point of view. Meanwhile, we get that every fuzzy frame equipped with the strong L-filter convex structure is an injective balanced L- S 0 -convex space and conversely, the specialization L-ordered set of an injective balanced L- S 0 -convex space is a fuzzy frame.