John Baez described the ``platonic idea of an equivalence'' or ``walking equivalence''. (This has also been called the ``free-living equivalence''.) He also describes the free-living adjoint equivalence, and the homotopy-theoretic relationship between the two. Similarly, one can construct the free-living adjunction. This was done in S. Schanuel and R. Street, The free adjunction, Cah. Top. Geom. Diff. 27:81-83, 1986. John also points out that one can consider not just equivalences, but 2-equivalences, 3-equivalences, and so on. The free-living pseudo-adjunction was constructed in Stephen Lack, A coherent approach to pseudomonads, Adv. Math. 152:179-202, 2000. from a rather different point of view to that of Schanuel and Street. Steve Lack.