nLab biadjunction

Context

2-Category theory

2-category theory

Contents

Idea

The notion of 2-adjunction of biadjunction is the higher generalization of the notion of adjunction from category theory to 2-category theory.

Definition

Given (possibly weak) 2-categories, $A$ and $C$, and (possibly weak) 2-functors $F:A\to C$ and $U:C\to A$, a biadjunction is given by specifying for each object $a$ in $A$ and each object $c$ in $C$ an equivalence of categories $C(F a,c)\cong A(a,U c)$, which is pseudonatural both in $a$ and in $c$.

There are several other characterizations of biadjointness.

Properties

If there is a biadjunction in this sense, it can be replaced by a biadjunction for which this equivalence of categories is an adjoint equivalence.

References

Revised on July 27, 2011 18:53:15 by Urs Schreiber (89.204.137.111)