Difference between revisions of "Bimorphism"
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(Created page with "==Definition== A ''bimorphism'' is a morphism or arrow in a category {{M|\mathscr{C} }}{{rITCTHS}}: * {{M|\xymatrix{ A \ar[r]^f & B} }} That is * both monic (cat...") |
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==Definition== | ==Definition== | ||
| − | A ''bimorphism'' is a [[morphism]] or [[arrow]] in a [[category]] {{M|\mathscr{C} }}{{ | + | A ''bimorphism'' is a [[morphism]] or [[arrow]] in a [[category]] {{M|\mathscr{C} }}{{rAITCTHS2010}}: |
* {{M|\xymatrix{ A \ar[r]^f & B} }} | * {{M|\xymatrix{ A \ar[r]^f & B} }} | ||
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]]'' | + | {{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]]''}} |
| − | + | ==References== | |
| − | {{ | + | <references/> |
| + | {{Category theory navbox}} | ||
Revision as of 15:24, 19 February 2016
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Definition
A bimorphism is a morphism or arrow in a category C[1]:
That is
Warning:A bimorphism need not be an isomorphism, when all bimorphisms in C are isomorphisms however, we say that C is balanced
References
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