= Path-space fibration
{title2=$\Omega X\to PX\to X$}
= Path fibration
{synonym}
Let $PX$ consist of paths starting at the chosen basepoint of $X$. Endpoint evaluation is a fibration $\Omega X\to PX\to X$, and $PX$ is contractible by shortening each path. Pulling it back along a map $Y\to X$ gives its <homotopy fibre>, after reversing the chosen path direction if needed. This makes an acyclic relative Sullivan algebra modelling $PX$ useful for explicit rational fibre calculations.
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