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Mar 6, 2021 at 21:13 vote accept Daniel Teixeira
Jan 30, 2021 at 1:26 comment added Tyler Lawson @DenisNardin Good point!
Jan 29, 2021 at 18:42 comment added Denis Nardin One can use a trick to answer your last question in the affirmative: an exact functor between stable ∞-category is an equivalence iff it induces an equivalence on the homotopy categories, and it's quite easy to see that both the dg-nerve of cofibrant complexes and the DK localization are stable, and that the functor preserves cofibers and direct sums (the latter because it is the DK-localization of a stable model category).
Jan 29, 2021 at 17:31 history edited Tyler Lawson CC BY-SA 4.0
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Jan 29, 2021 at 17:26 history answered Tyler Lawson CC BY-SA 4.0