terminal object as zero object in a pointed category

Let \(\mathcal{C}\) be a pointed category and \(1 \in \mathrm{Ob}(\mathcal{C})\) the terminal object Then \(1 \cong 0\) is canonically isomorphic to the zero object

follows from uniqueness of the terminal object up to unique isomorphism hom-functor and isomorphisms under functors