\begin{definition}[Definition:Isomorphism of Categories/Isomorphic Categories]
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 $\mathbf C \cong \mathbf D$.
\end{definition}