categories: free-living/platonic/walking equivalences and adjunctions

[Steve Lack <stevel@maths.usyd.edu.au>]

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.