Definition:Equivalence of Categories/Equivalent Categories

Definition
Let $\mathbf C$ and $\mathbf D$ be metacategories. Let there exist an equivalence of categories between $\mathbf C$ and $\mathbf D$.

Then $\mathbf C$ and $\mathbf D$ are said to be equivalent, denoted $\mathbf C \simeq \mathbf D$.

Also see

 * Definition:Isomorphic Categories