Definition:Isomorphism of Categories/Isomorphic Categories

Definition
Let $\mathbf C$ and $\mathbf D$ be metacategories. Let $F: \mathbf C \to \mathbf D$ be an isomorphism of categories.

Then $\mathbf C$ and $\mathbf D$ are said to be isomorphic, and we write $\mathbf C \cong \mathbf D$.

Also see

 * Equivalent Categories
 * Isomorphism of Categories