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?
The category of adjoint functors
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category-theory
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2No particular reason, just playing :) – 2012-09-08