Difference between revisions of "Bimorphism"

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==Definition==
 
==Definition==
 
A ''bimorphism'' is a [[morphism]] or [[arrow]] in a [[category]] {{M|\mathscr{C} }}{{rAITCTHS2010}}:
 
A ''bimorphism'' is a [[morphism]] or [[arrow]] in a [[category]] {{M|\mathscr{C} }}{{rAITCTHS2010}}:
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That is
 
That is
 
* both [[monic (category theory)|monic]] and [[epic (category theory)|epic]]
 
* both [[monic (category theory)|monic]] and [[epic (category theory)|epic]]
{{Warning|A ''bimorphism'' need not be an ''[[isomorphism]]'', when all bimorphisms in {{M|\mathscr{C} }} are isomorphisms however, we say that  {{M|\mathscr{C} }}  is ''[[balanced (category theory)|balanced]]''}}
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{{Warning|A ''bimorphism'' need not be an ''[[isomorphism (category theory)|isomorphism]]'', when all bimorphisms in {{M|\mathscr{C} }} are isomorphisms however, we say that  {{M|\mathscr{C} }}  is ''[[balanced (category theory)|balanced]]''}}
  
 
==References==
 
==References==
 
<references/>
 
<references/>
 
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Latest revision as of 14:23, 13 March 2016

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Definition

A bimorphism is a morphism or arrow in a category [ilmath]\mathscr{C} [/ilmath][1]:

  • [ilmath]\xymatrix{ A \ar[r]^f & B} [/ilmath]

That is

Warning:A bimorphism need not be an isomorphism, when all bimorphisms in [ilmath]\mathscr{C} [/ilmath] are isomorphisms however, we say that [ilmath]\mathscr{C} [/ilmath] is balanced

References

  1. An Introduction to Category Theory - Harold Simmons - 1st September 2010 edition