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Can a category structure be defined on the collection $Adj(\mathbf C,\mathbf D)$ of all pairs of adjoint functors $ (F\colon\mathbf C\to \mathbf D)\dashv (G\colon \mathbf D\to \mathbf C)$ in such a way that the correspondence $\mathbf{Cat}\times\mathbf{Cat}\to \mathbf{Cat}\colon (\mathbf C,\mathbf D)\mapsto Adj(\mathbf C,\mathbf D)$ is functorial?

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    No particular reason, just playing :)2012-09-08

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