\begin{definition}[Definition:Equivalence of Categories/Equivalent Categories]
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 $\mathbf C \simeq \mathbf D$.
\end{definition}