Difference between revisions of "Isomorphism"
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{{WotWAnnounce|week=March 12-19}} | {{WotWAnnounce|week=March 12-19}} | ||
| − | 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 | + | 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. |
Revision as of 11:25, 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 
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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