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Feb 10, 2022 at 19:43 comment added Tim Campion Just to clarify, the conclusions are (as I understand) the following. Let $A$ be a Grothendieck abelian category: (2) For any presentable $\infty$-category $C$, there is an equivalence between (i) functors $A \to C$ which preserve coproducts and filtered colimits, and carry short exact sequences to cofiber sequences and (ii) functors $\check D (A)_{\geq 0} \to C$ which preserve colimits. (1) If $C$ is moreover stable, then we may replace $\check D(A)_{\geq 0}$ with its stabilization $\check D(A)$ in the statement of (2).
Oct 8, 2017 at 9:09 vote accept Yonatan Harpaz
Oct 6, 2017 at 22:07 answer added Jacob Lurie timeline score: 13
Oct 6, 2017 at 14:28 history asked Yonatan Harpaz CC BY-SA 3.0