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In category theory, the expression $f\circ g=h$ ($\circ$ being the binary composition "function" on the class of morphisms) suggests that the morphism $h$ is unique when it clearly needn't be. Do we not have to define an equivalence relation on the set of morphisms using the $hom$ class?

  • 7
    Why do you think it "needn't be"?2012-11-05
  • 0
    $f$ is a particular arrow. $g$ is a particular arrow. $f\circ g$ is another arrow. What is the problem?2012-11-06

2 Answers 2