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Mar 24, 2019 at 7:45 comment added Simon Henry Yes of course ! I know. But as you suspected, I was hopping for more elementary references that could also be read by people only familiar with ordinary category theory.
Mar 24, 2019 at 7:08 comment added Denis Nardin It's certainly not what you have in mind, but I think it might be worth mentioning that Lurie's work does cover this example too (although I don't think he works out the details in his book): $\mathrm{Set}$ is an idempotent algebra in $\mathrm{Pr}^L$ and modules over it are precisely presentable 1-categories.
Mar 23, 2019 at 15:02 history edited Simon Henry CC BY-SA 4.0
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Mar 23, 2019 at 14:23 vote accept Simon Henry
Mar 23, 2019 at 14:02 history became hot network question
Mar 23, 2019 at 13:51 answer added Alexander Campbell timeline score: 16
Mar 23, 2019 at 11:56 history asked Simon Henry CC BY-SA 4.0