nLab local adjunction

Redirected from "local adjunctions".
Contents

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

Contents

Idea

Let π’œ\mathscr{A} and ℬ\mathscr{B} be bicategories.

A local adjunction between π’œ\mathscr{A} and ℬ\mathscr{B} comprises lax functors L:π’œβ†’β„¬L \colon \mathscr{A} \to \mathscr{B} and R:β„¬β†’π’œR \colon \mathscr{B} \to \mathscr{A} and a family of adjunctions

ℬ(LA,B)β‡„π’œ(A,RB) \mathscr{B}(L A, B) \rightleftarrows \mathscr{A}(A, R B)

between hom-categories, natural in AA and BB.

References

Local adjunctions are defined in:

Last revised on April 25, 2023 at 04:07:30. See the history of this page for a list of all contributions to it.