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Yes. This follows directly from 5.1 in Strong conceptual completeness for first-order logic by Makkai (1988, Annals of Pure and Applied Logic, doi:10.1016/0168-0072(88)90019-X).
Yes. This follows directly from 5.1 in Strong conceptual completeness for first-order logic by Makkai.
Yes. This follows directly from 5.1 in Strong conceptual completeness for first-order logic by Makkai (1988, Annals of Pure and Applied Logic, doi:10.1016/0168-0072(88)90019-X).
