categories: Re: Exact adjunctions

[Dusko Pavlovic <dusko@kestrel.edu>]

the following is in the appendix of my paper Maps II

ftp://ftp.kestrel.edu/pub/papers/pavlovic/mapsII.ps.gz

Lemma. Let R be a bicategory. Suppose we are given 0-cells A and B,
1-cells F:A->B and G:B->A and 2-cells h:id_A --> FG and e:GF -->id_B.
Then F is left adjoint to G if and only if the 2-cells

   hF;Fe : F --> FGF --> F
   Gh;eG : G --> GFG --> G

are both split epi (or split mono).

the paper was published in 1996, but this particular lemma (with the
proof) was announced on this list shortly after i arrived to mcgill,
probably in january or february of 1992.

-- dusko