nLab local adjunction

This page is about a structure on pairs of bicategories. Beware that parametric right adjoints are, confusingly, also sometimes called “local right adjoints”. See at locally.

Idea

Let $\mathscr{A}$ and $\mathscr{B}$ be bicategories.

A local adjunction between $\mathscr{A}$ and $\mathscr{B}$ comprises lax functors $L \colon \mathscr{A} \to \mathscr{B}$ and $R \colon \mathscr{B} \to \mathscr{A}$ and a family of adjunctions

$$\mathscr{B}(L A, B) \rightleftarrows \mathscr{A}(A, R B)$$

between hom-categories, natural in $A$ and $B$.

Related concepts

• adjunction

• 2-adjunction

• biadjunction

• pseudoadjunction

References

Local adjunctions are defined in:

• Colin Barry Jay. Local adjunctions. Journal of Pure and Applied Algebra 53 3 (1988) 227-238 [doi:10.1016/0022-4049(88)90124-7]