ScalingStacks

Remark 8.2.19. Consider $Z$ the singular curve quotient of oriented ${\mathbf{R}}$ by the identification of two points. Take $M$ to be the single exceptional point of $Z$. The construction above applied to ${\mathcal{S}}_{M}^{\bullet}(Z)$ gives a category where going twice around the circle, avoiding the loop, is non-zero (cf picture below), while it is not represented by a smooth path in $Z_{\xi}$. Theorem 8.2.18 does not hold because $M$ is too small.