Prove a square is a pullback

Question

Let $C$ an abelian category, and consider the following diagram: $$ \require{AMScd} \begin{CD} P @> \beta_1 >> A_1 \\ @V \beta_2 VV @VV \alpha_1 V \\ A_2 @> \alpha_2 >> A \, \end{CD} $$ Prove that if $\alpha_1$ is an epimorphism, then the square is a pullback.

I'm stuck, any hint, please? :(

Answer 1

The statement is false. As a counterexample, we consider the following diagram in $\mathbf{Ab}$: $$ \require{AMScd} \begin{CD} ℤ @>>> 0 \\ @VVV @VVV \\ 0 @>>> 0 \end{CD} $$