Difference between revisions of "Isomorphism"

(Better to use category theory terminology)
(need that the inverse is a homomorphism)
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{{WotWAnnounce|week=March 12-19}}
 
{{WotWAnnounce|week=March 12-19}}
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.
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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 as two superficially different versions of the same object.  Isomorphic objects cannot be distinguished by Universal Mapping Properties.
  
  

Revision as of 12:24, 15 March 2008

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

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 as two superficially different versions of the same object. Isomorphic objects cannot be distinguished by Universal Mapping Properties.


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