ScalingStacks

Remark 11.3. Note that if the functor $i\colon\mathcal{R}\to\Upsilon_{n}$ is fully-faithful, then condition (R.3) is automatic. Note also that (R.3) and (R.4) together imply that the presheaves $i^{*}(C_{k})$ on $\mathcal{R}$ are each $T$-equivalent to representables $R_{k}$.