Thanks, it is indeed true. Regularity is also preserved under coslicing (what about more general comma constructions?), so one can derive that the cos...

Another observation, don't take it as well-informed: the poset of essential localisations is usually not as well-behaved as one would expect; probably...

Can you phrase more in detail the question? I see what is a "level" from nLab, though some more context would help potential readers. I would say yo...

@matteocapucci You already found a way to rewrite the left and right Kan extensions of $f$; if you're interested in the bigger picture, the request th...