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Oct 1 at 17:58 comment added varkor (I believe I have a characterisation of both conditions now. I will write up a proof later.)
Oct 1 at 12:16 comment added varkor A relevant reference for cartesian closure is Proposition 20 of Bastiani–Ehresmann's Categories of sketched structures.
Oct 1 at 11:27 comment added varkor This issue is discussed in §4 of Borceux–Pedicchio's A characterization of quasi-toposes.
Sep 27 at 11:48 comment added varkor I believe it should be possible to extract a characterisation of the locally cartesain closed locally presentable categories from Theorem 7.25 of Street's Cosmoi of internal categories, although note that footnote 2 ibid. seems in contradiction with mathoverflow.net/questions/294108/….
Oct 24, 2020 at 7:48 answer added Ivan Di Liberti timeline score: 2
Oct 24, 2020 at 6:19 answer added Ben MacAdam timeline score: 3
Oct 23, 2020 at 23:10 history asked varkor CC BY-SA 4.0