nLab local adjunction

Let 𝒜\mathscr{A} and \mathscr{B} be bicategories. A local adjunction between 𝒜\mathscr{A} and \mathscr{B} comprises lax functors L:𝒜L \colon \mathscr{A} \to \mathscr{B} and R:𝒜R \colon \mathscr{B} \to \mathscr{A} and a family of adjunctions (LA,B)𝒜(A,RB)\mathscr{B}(L A, B) \rightleftarrows \mathscr{A}(A, R B) natural in AA and BB.

References

Local adjunctions are defined in:

Colin Barry Jay?. Local adjunctions. Journal of Pure and Applied Algebra 53.3 (1988): 227-238.

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