Proposition 6.1 (05UE) · ScalingStacks

Proposition 6.1. If $C$ is a small category, then the classifying diagram $NC$ of (3.5) is a complete Segal space.

Proof. This follows from (3.6) and (3.9), together with the fact that $(NC)_{\hoequiv}$ is isomorphic to $\nerve\iso(C^{I[1]})$ and the fact that the natural inclusion $\iso C\rightarrow\iso(C^{I[1]})$ is an equivalence of categories. ∎