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Dec 5, 2022 at 0:17 comment added Emily By the way, when you mentioned marked simplicial sets, Lurie's scaled simplicial sets immediately came to my mind, and I was eventually able to track a reference that fully spells out this point, Remark 1.21 of arXiv:1911.01905 (I'm adding this here since other people might find it useful). Thanks so much again!
Dec 5, 2022 at 0:17 comment added Emily Hi Simon, thank you so much for your reply, it perfectly clarifies a lot of things I had in mind when I asked this question! =)
Dec 5, 2022 at 0:17 vote accept Emily
Dec 3, 2022 at 18:31 history answered Simon Henry CC BY-SA 4.0