30 Nov
2009
30 Nov
'09
11:34 a.m.
Dear Claudio,
If F is left adjoint to G : D --> C and there is a natural isomorphism FG --> 1_D (not necessarily the counit), then G is full and faithful.
A proof of the (dual) claim you find as the proof of Lemma 8.1 of my course on basic category theory www.mathematik.tu-darmstadt.de/~streicher/CTCL.pdf.gz on p.45. Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]