I have the following situation: I have an adjunction F:C<->D:G such that the left adjoint F is faithful (but not full), and I would like to characterize its essential image. If F were full, its image would be precisely those objects of D for which the co-unit is an isomorphism. Is there an analogous description for the case that F is only faithful? If it matters, in the situation I am looking at, I have a faithful functor j:A -> B, and I am trying to characterize the essential image of its prolongation j_!:Psh(A) \to Psh(B). I welcome any comments. Thank you for your time, Dave Carchedi [For admin and other information see: http://www.mta.ca/~cat-dist/ ]