An isomorphism is a bijective homomorphism whose inverse is also homomorphism. If $A$ and $B$ are objects in a certain category such that there exists an isomorphism $A\to B$, then $A$ and $B$ are said to be isomorphic. Informally speaking, two isomorphic objects can be considered to be two superficially different versions of the same object. Isomorphic objects cannot be distinguished by universal mapping properties.

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