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Evan Patterson (Jan 27 2023 at 04:44):A very useful fact is that limits in functor categories are computed pointwise. Is a similar statement true for limits in double functor categories? If so, is there a reference for it? I am most interested in the case of pseudo double functors between pseudo double categories, with morphisms the usual natural transformations (whose data are families of arrows and cells indexed by objects and proarrows, respectively).
El Mehdi Cherradi (Jan 27 2023 at 12:24):I would say yes in both case because this looks like it should fit into a suitable homotopy limits framework (where it would follow from the pointwise computation of homotopy Kan extensions), but this is just an intuition.