Bimorphism

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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

v • d • e
 
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
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