For $A$-modules and homomorphisms $0\to M′\stackrel{u}{\to}M\stackrel{v}{\to}M′′\to 0$ is exact iff for all A-modules N, the sequence
$0 \to Hom(M′′,N)\stackrel{\bar{v}}{\to} Hom(M,N)\stackrel{\bar{u}}{\to} Hom(M′,N)$ is exact.
How $\bar{u}$ and $\bar{v}$ are defined ? How do I prove that the sequence is exact at Hom(M′′,N) and Hom(M′,N)?
thanks for any help or hints