# Difference between revisions of "Isomorphism"

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− | An '''isomorphism''' is a [[bijective]] [[homomorphism]] whose inverse is also homomorphism. If <math>A</math> and <math>B</math> are objects in a certain category such that there exists an isomorphism <math>A\to B</math>, then <math>A</math> and <math>B</math> 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. | + | An '''isomorphism''' is a [[bijective]] [[homomorphism]] whose inverse is also homomorphism. If <math>A</math> and <math>B</math> are objects in a certain [[Category (category theory)|category]] such that there exists an isomorphism <math>A\to B</math>, then <math>A</math> and <math>B</math> 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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[[Category:Abstract algebra]] | [[Category:Abstract algebra]] | ||

+ | [[Category:Category theory]] |

## Latest revision as of 21:13, 2 September 2008

An **isomorphism** is a bijective homomorphism whose inverse is also homomorphism. If and are objects in a certain category such that there exists an isomorphism , then and 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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