ScalingStacks

Proposition 7.3.19. Let $Z$ be a curve with an admissible relation $\sim$ and let $q:Z\to Z/\!\!\sim$ be the quotient map. The functor $q^{\#}:\operatorname{add}\nolimits({\mathcal{S}}(Z/\!\!\sim,1))\to\operatorname{add}\nolimits({\mathcal{S}}(Z,1))$ is faithful.