Composition of a unique arrow with the inverse of another Suppose we have the arrows $u:T \rightarrow Q$, $v:T \rightarrow P$ and $f:P \rightarrow Q$.  Furthermore, suppose $u$ is unique and $f$ is iso.
I understand that we can say that $v = u;f^{-1}$, but do we have enough information that $v$ is also unique?
I believe that $v$ is unique, but I'm not sure why.  I think it is because - by  the uniqueness of inverses - $f^{-1}$ is unique, and that when it is composed with another unique arrow ($u$), then the composition $u;f^{-1}$ must also be unique.
Can anyone confirm whether this is the case, please?

Yes this is true. Once you have two arrows (the same thing as two uni ue arrows) you can compose them (composition being a function). 
