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.

Thomas M. Fiore, Pseudo limits, biadjoints, and pseudo algebras: categorical foundations of conformal field theory, Memoirs of the American Mathematical Society 182 (2006), no. 860. 171 pages, MR2007f:18006, math.CT/0408298

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