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]].  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.
 
  
  

Revision as of 21:07, 20 March 2008

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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