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Timeline for HTT, Remark 4.2.4.5

Current License: CC BY-SA 4.0

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Apr 17 at 9:37 vote accept Ken
Feb 16, 2023 at 10:11 comment added Ken Thanks! It does show that $N((\mathbf{A}^{\mathcal{C}})_{\mathrm{proj}}^{\circ})$ and $N((\mathbf{A}^{\mathcal{C}})_{\mathrm{inj}}^{\circ})$ can be joined by a zig-zag of weak categorical equivalences. However, I do not yet understand why the map $$ N((\mathbf{A}^{\mathcal{C}})_{\mathrm{inj}}^{\circ})\to\operatorname{Fun}(S,N(\mathbf{A}^{\circ})) $$ is an equivalence of $\infty$-categories. Can you elaborate on this?
Feb 16, 2023 at 5:31 history answered Dmitri Pavlov CC BY-SA 4.0