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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


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