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started a stub for ambidextrous adjunction, but not much there yet
also stubs for Frobenius monoid and Frobenius monad, just for completeness; added cross-links
Will any equivalence between the two adjoints do, or should it be compatible with the units and counits in some way?
I don’t think there is any compatibility that you can ask for. The specified equivalence between the two adjoints should be regarded as part of the structure, i.e. being an ambijoint is not just a mere property of a functor.
I have added a paragraph Properties – Fiberwise characterization of ambid. Kan extension in order to record the corresponding result by Hopkins-Lurie.
(Eventually there should maybe be a standalone section/entry on ambidextrous Kan extensions.)
added cross-link with bireflective subcategory and pointer to:
Functor $G$ which has a left and right adjoint which are equivalent is said to be Frobenius functor.
Connection to Hopf adjunctions
added pointer to the early article
where ambidextrous adjunctions were (first?) discussed under the name “strongly adjoint pair”
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