Cancellation laws for function composition Okay I was asked to make a conjecture about cancellation laws for function composition. I figured it would go something like "For all sets $A$ and functions $g: A \rightarrow B$ and $h: A \rightarrow B$, $f \circ g = f \circ h$ implies that $g=h$." 
I'm pretty sure $g=h$ isn't always true, but is there a property of $f$ that makes this true? 

Notice that if there are distinct $b_1,b_2\in B$ such that $f(b_1)=f(b_2)$, you won’t necessarily be able to cancel $f$: there might be some $a\in A$ such that $g(a)=b_1$ and $h(a)=b_2$, but you’d still have $(f\circ g)(a)=(f\circ h)(a)$. Thus, you want $f$ to be injective (one-to-one). Can you prove that that’s sufficient?
