nLab
biadjunction

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, AA and CC, and (possibly weak) 2-functors F:ACF:A\to C and U:CAU:C\to A, a biadjunction is given by specifying for each object aa in AA and each object cc in CC an equivalence of categories C(Fa,c)A(a,Uc)C(F a,c)\cong A(a,U c), which is pseudonatural both in aa and in cc.

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)