Difference between revisions of "Isomorphism"

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{{WotWAnnounce|week=March 12-19}}
 
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An '''isomorphism''' is a [[bijective]] [[homomorphism]].  If <math>A</math> and <math>B</math> are structures of a certain species such that there exists an isomorphism <math>A\to B</math>, then <math>A</math> and <math>B</math> are said to be '''isomorphic''' structures of that species.  Informally speaking, two isomorphic structures can be considered as two superficially different versions of the same structure.
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An '''isomorphism''' is a [[bijective]] [[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 as two superficially different versions of the same object.  Isomorphic objects cannot be distinguished by Universal Mapping Properties.
  
  

Revision as of 12:23, 15 March 2008

This is an AoPSWiki Word of the Week for March 12-19

An isomorphism is a bijective 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 as two superficially different versions of the same object. Isomorphic objects cannot be distinguished by Universal Mapping Properties.


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