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?
Category Theory: Is it necessary to define an equivalence relation on the class of morphisms?
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category-theory
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7Why do you think it "needn't be"? – 2012-11-05
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0$f$ is a particular arrow. $g$ is a particular arrow. $f\circ g$ is another arrow. What is the problem? – 2012-11-06