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

• Definition:Equivalent Categories
• Definition:Isomorphism of Categories

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.

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