Abstract: We considered representation problems of Z-Quantale. Firstly, we proved that any unital Z-Quantale was isomorphic to the Z-Quantale formed by its strong self-continuous maps. Secondly, we  proved that any  unital Z-Quantale was isomorphic to a relation Z-Quantale. Finally, we discussed the relationship between the category of unital Z-Quantale and the category of relation Z-Quantale, and  proved that the category of unital Z-Quantale was equivalent to the category of relation Z-Quantale.

Key words: Z-Quantale,  ,  , unital Z-Quantale, Z-Quantale isomorphism, representation theorem