  In this paper, we consider $\text{C}^*$-algebras with the ideal property (the
ideal property unifies the simple and real rank zero cases). We define two
categories related the invariants of the $\text{C}^*$-algebras with the ideal
property. And we showed that these two categories are in fact isomorphic. As a
consequence, the Elliott's Invariant and the Stevens' Invariant are isomorphic
for $\text{C}^*$-algebras with the ideal property.
