There are many ways to give a definition of a biadjunction. For instance, one may say that a pseudofunctor $F:\mathcal{C}\rightarrow \mathcal{D}$ is left biadjoint to $G:\mathcal{D}\rightarrow \mathcal{C}$ if there are pseudo-natural transformations $\eta:Id_{\mathcal{C}}\rightarrow GF$ and $\epsilon:FG\rightarrow Id_{\mathcal{D}}$ satisfying the triangle identities up to invertible modifications. Now, there is also a coherent version of the latter definition (see [Gurski](https://arxiv.org/abs/1102.0979)), where the modifications witnessing the triangle identites satisfy the swallowtail equations. The ncatlab entry for biadjunctions (and my intuition) makes me believe that every biadjunction can be made coherent, but I haven't been able to find a reference in the litterature. Does anybody know where to find one?