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


Overview of the concepts of Category Theory


Key objects


[ilmath]\xymatrix{ & \text{Arrow} \\ \text{Monic} \ar@{^{(}>}[ur] & & \text{Epic} \ar@{^{(}>}[ul] \\ & \text{Bimorphism} \ar@{^{(}>}[ur] \ar@<0.5ex>@{^{(}>}[ul] \\ {\begin{array}{c}\text{Section}\\ \text{(Split monic)} \end{array} } \ar@{^{(}>}[uu] & & {\begin{array}{c}\text{Retraction}\\ \text{(Split epic)} \end{array} } \ar@<0.75ex>@{^{(}>}[uu] \\ & \text{Isomorphism} \ar@{^{(}>}[ur] \ar@<0.5ex>@{^{(}>}[ul] \ar@{^{(}>}[uu] }[/ilmath]


Typical morphism types (see diagram on right)



Key objects



Primitive constructs



Key constructs



Important examples



Trivial category examples



Common categories


