  We introduce partially lax limits of infinity-categories, which interpolate
between ordinary limits and lax limits. Most naturally occurring examples of
lax limits are only partially lax; we give examples arising from enriched
categories and operads. Our main result is a formula for partially lax limits
and colimits in terms of the Grothendieck construction. This generalizes a
formula of Lurie for ordinary limits and of Gepner-Haugseng-Nikolaus for fully
lax limits.
