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Oct 24, 2020 at 19:25 comment added varkor Day's reflection theorem tells us that the LFP category $\mathscr C$ is cartesian-closed iff the reflector is cartesian: how can we characterise the corresponding category of finitely presentable objects for $\mathscr C$ using this?
Oct 24, 2020 at 8:09 comment added Ivan Di Liberti This answer is coherent with Street's Thm. 3.11 in Cosmoi of internal categories.
Oct 24, 2020 at 6:19 history answered Ben MacAdam CC BY-SA 4.0