Is there an explicit proof anywhere in the literature that filtered 2-colimits commute with finite 2-limits (all meant in the weak bicategorical sense) in the 2-category of groupoids? I have only been able to find a handful of papers about filtered 2-colimits, notably Dubuc and Street's [A construction of 2-filtered bicolimits of categories](https://arxiv.org/abs/math/0605304), and have not found this result in any of them.


Of course one could try to deduce this from $\infty$-categorical results, but the latter proofs are also often sketchy, and in the case of groupoids it ought to be possible to give a concrete constructive proof.



Filtered 2-colimits commute with finite 2-limits
Two relevant papers are:


* Dupont's [Interchange of filtered 2-colimits and finite 2-limits](https://arxiv.org/abs/0904.1553).
* Canevali's [2-filtered bicolimits and finite weighted bilimits commute in Cat](http://cms.dm.uba.ar/academico/carreras/licenciatura/tesis/2016).


The former proves that finite conical pseudolimits and filtered pseudolimits commute in $\mathbf{Cat}$; whereas the latter proves the analagous result for finite weighted bilimits and filtered bicolimits.


It may be that these are enough to recover commutivity in $\mathbf{Grpd}$ for the cases in which you are interested.


