I'm trying to solve the following exercise: Let $\lambda: \Delta [1]\to K$ be be a map of simplicial sets (which we can think of as a path) where K is a Kan complex. Prove there exists a path $\lambda^{-1}: \Delta [1]\to K$ such that $\lambda^{-1}(0)=\lambda(1)$ and $\lambda^{-1}(1)=\lambda(0)$....