In the book 'Sheaf theory' by Tennison, exercise 1.9 asks to prove that if $G$ is an abelian sheaf then $G(\phi)=\{ 0 \}$. I have been unsuccessfully trying to prove this and the following seems to be a counter example to me :
Let X be the space consisting of a singleton set {p}. Define an abelian sheaf $G$ by : $G(X)=\{ 0 \} $ , $G(\phi)=\mathbb{Z}$, and the restriction maps to be : $\rho^{X}_{X}=0$, $\rho^{\phi}_{\phi}=id_{\mathbb{Z}}$, $\rho^{X}_{\phi}=0$.
All the sheaf axioms seem to be valid. Where am I going wrong ? Thanks.