From this is follows that the identity morphism for \\(A\\) must be _unique_. For suppose that there were two identity morphisms \\(I_1,I_2\\) for \\(A\\). Then consider the linear tree which chains \\(I_1\\) into \\(I_2\\). The result of splicing \\(I_1\\) out of the chain is \\(I_2\\), and the result of splicing \\(I_2\\) out of the chain is \\(I_1\\). By the identity requirement, these must be equal.