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Jan 7, 2021 at 16:06 comment added john Hi Chris. I suspect that the category of monoidal categories and lax monoidal functors does not have split idempotents (and so would lack filtered colims.)
Jan 6, 2021 at 10:58 comment added Chris Heunen That's great info, thanks John! Would this reduction to Cat work with lax monoidal functors too?
Jan 5, 2021 at 21:22 history answered john CC BY-SA 4.0