nLab
strict 2-adjunction

Given strict 2-categories, A and C, and strict 2-functors F:AC and U:CA, a strict 2-adjunction is given one of the following two equivalent means:

  • an isomorphism of categories C(Fa,c)A(a,Uc) for each object a in A and object c in C, which is strict 2-natural both in a and in c;

  • a strict 2-natural 2-transformations of 2-functors unit η:Id AUF, and counit ϵ:FUId B, satisfying the triangle identities strictly.

There are more relaxed forms of 2-adjunctions, namely the pseudoadjunctions and biadjunctions, both of which can be considered for 2-functors of either strict or weak 2-categories.

Created on September 29, 2010 14:52:31 by Zoran Škoda (161.53.130.104)