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2 Proof that for any function $f:Ato B$ there exists a set $C$ and two functions $g:Ato C,h:Cto B$ not equal to $f$ such that $f=hcirc g$ ? I really have no clue how to tackle this problem. I have strong evidence to conclude this is true, but I don't know how to prove it. I think this may be solved using category theory, knowing if in the category Set , for any morphism $f:Alongrightarrow B$ , there are two morphisms such that their composition equals $f$ . The axioms for category tells the opposite, that for any two morphism there exists their composition morphism, but is it true the other way around in this context? And if this is not true, what condition does $f$ need to have in order to not have this property? functions category-theory