Change of basepoint isomorphism ($u_{\#}$)

Let $u$ be a path from $x_0$ to $x_1$. Traversing paths from left to right gives an isomorphismConcatenation and cancellation of a path with its reverse prove the homomorphism property and show that $\bar{u}$ supplies its inverse. A different connecting path changes this isomorphism by an inner automorphism, so it need not be canonical.