22 Nov
2001
22 Nov
'01
1:15 a.m.
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