« first day (1664 days earlier)      last day (1051 days later) » 

12:30 AM
@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
@OmarAntolín-Camarena i feel I should be fair and point out that this result, at least as folklore, is a lot older than that
 
 
14 hours later…
2:46 PM
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
 
3:14 PM
@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...
 

« first day (1664 days earlier)      last day (1051 days later) »