@AaronMazel-Gee and to make matters worse, this is delicate: it's very false when you switch to coalgebras instead of algebras unless the discrete coalgebra is flat over the base

I vaguely remember there being a theorem saying that the total ∞-category of a presentable fibration with presentable base is presentable. Does anyone know a reference for it? Bonus points if know hypotheses to get the total category to be compactly generated

@DenisNardin That's in my paper with Gepner and Nikolaus on "lax colimits and free fibrations", generalizing a result of Makkai and Paré for 1-categories. We did not consider bounds on the accessibility, but the construction is rather explicit, so it might be doable.

Thank you! Time to get my hands dirty with the proof...