ScalingStacks

Definition 7.4.1. A parametrized braid $I\to J$ is a family $\vartheta=(\vartheta_{s})_{s\in I}$ where $\vartheta_{s}$ is an admissible path in $Z$ with $\vartheta_{s}(0)=s$ and such that $s\mapsto\vartheta_{s}(1)$ defines a bijection $\chi(\vartheta):I\mathrel{\mathop{\kern 0.0pt\to}\limits^{\sim}}J$ . A braid $I\to J$ is a homotopy class of parametrized braids, i.e., a family of admissible homotopy classes of paths.