Definition:Isomorphism of Categories/Isomorphic Categories
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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
Linguistic Note
The word isomorphism derives from the Greek morphe (μορφή) meaning form or structure, with the prefix iso- meaning equal.
Thus isomorphism means equal structure.