Let $F\_0 : C \to D$ be a functor. If it exists, let $G\_0 : D \to C$ be its left adjoint. If it exists, let $F\_1 : C \to D$ be **its** left adjoint. And so forth. In situations where the infinite sequence $(F\_0, G\_0, F\_1, G\_1, ...)$ exists, when is it periodic? Aperiodic? (Feel free to replace all "lefts" by "rights," of course.)



Iterated adjoint functors
<http://www.springerlink.com/content/pmj5074147116273/> considers sequences of adjoint functors just like you describe.


