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Is there a theory of homotopy coherent adjunctions between $\mathcal{A}_{\infty}$-categories? By this I mean at least a definition of what an adjunction is and a construction of the corresponding unit/counit.

I couldn't find any reference in the literature. Thank you very much in advance.

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    $\begingroup$ Riehl and Verity study the free homotopy coherent adjunction as a simplicial category, see below; it should be possible to make the correct definition via this and by taking an appropriate nerve of the $A_\infty$-category or an appropriate realization of the simplicial category. arxiv.org/abs/1310.8279 $\endgroup$ Jan 25, 2020 at 2:44

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